Peter Lancaster

• The solution of linear and nonlinear equations in matrices and operators.
• Diverse problems of linear algebra and its applications, perturbation theory
• The analysis of numerical methods relevant to spectral and factorization problems for matrix and operator functions stimulated by problems in the theory of vibrations, systems theory and control

Book

• Gohberg, Israel, Lancaster, Peter and Rodman, Leiba. Indefinite Linear Algebra with Applications Birkh\"auser Verlag, 2005. 357. Print.
• Lancaster, Peter. My life and mathematics 130. Birkh\"auser, 2002. 1-7. Print.
• Lancaster, Peter. The role of the {H}amiltonian in the solution of algebraic {R}iccati equations 25. Birkh\"auser, 1999. 157-172. Print.
• Lancaster, Peter, Maroulas, John and Zizler, Peter. The numerical range of selfadjoint matrix polynomials 106. Birkh\"auser, 1998. 291-304. Print.
• Lancaster, Peter and Matsaev, V.. Definitizable {$G$}-unitary operators and their applications to operator polynomials 87. Birkh\"auser, 1996. 222-232. Print.
• Lancaster, Peter and Matsaev, V.. Perturbations of {$G$}-selfadjoint operators and operator polynomials with real spectrum 87. Birkh\"auser, 1996. 207-221. Print.
• Lancaster, Peter and Salkauskas, Kes. Transform methods in applied mathematics , John Wiley \& Sons Inc., 1996. xii+332. Print.
• Lancaster, Peter and Rodman, Leiba. Algebraic {R}iccati equations , The Clarendon Press Oxford University Press, 1995. xviii+480. Print.
• Lancaster, Peter and Rodman, Leiba. Solutions of the continuous and discrete-time algebraic {R}iccati equations: a review , Springer, 1991. 11-51. Print.
• Lancaster, Peter and Ye, Qiang. Variational properties and {R}ayleigh quotient algorithms for symmetric matrix pencils 40. Birkh\"auser, 1989. 247-278. Print.
• Koltracht, I. and Lancaster, Peter. Condition numbers of {T}oeplitz and block {T}oeplitz matrices 18. Birkh\"auser, 1986. 271-300. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. Invariant subspaces of matrices with applications , John Wiley \& Sons Inc., 1986. xviii+692. Print.
• Lancaster, Peter and Salkauskas, Kes. Curve and surface fitting Academic Press Inc. [Harcourt Brace Jovanovich Publishers], 1986. xii+280. Print.
• Lancaster, Peter and Tismenetsky, Miron. The theory of matrices , Academic Press Inc., 1985. xv+570. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. A sign characteristic for selfadjoint rational matrix functions 58. Springer, 1984. 363-369. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. Matrices and indefinite scalar products 8. Birkh\"auser Verlag, 1983. xvii+374. Print.
• Barnett, S. and Lancaster, Peter. Matrices having striped inverse Hemisphere, 1982. 333-336. Print.
• Lancaster, Peter. A review of some recent results concerning factorization of matrix and operator valued functions 80. Dekker, 1982. 117-139. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. Matrix polynomials Academic Press Inc. 1982. SIAM, 2009., 1982. xiv+409. Print.
• Lancaster, Peter. Composite methods for generating surfaces 49. Reidel, 1979. 91-102. Print.
• Lancaster, Peter. Moving weighted least-squares methods 49. Reidel, 1979. 103-120. Print.
• Lancaster, Peter. A review of numerical methods for eigenvalue problems nonlinear in the parameter Birkh\"auser, 1977. 43-67. Internat. Schriftenreihe zur Numer. Math., Vol. 38. Print.
• Lancaster, Peter and Watkins, David S.. Interpolation in the plane and rectangular finite elements Birkh\"auser, 1976. 125-145. Internat. Ser. Numer. Math., Vol. 31. Print.
• Terray, John and Lancaster, Peter. A boundary value problem from the study of heat transfer Birkh\"auser, 1975. 303-308. Internat. Schriftenreihe Numer. Math., Band 27. Print.
• Lancaster, Peter. Spektraleigenschaften von {O}peratorfunktionen Birkh\"auser, 1970. 53-60. Internat. Schriftenreihe Numer. Math., Vol. 15. Print.
• Lancaster, Peter. Theory of matrices Academic Press, 1969. xii+316. Print.
• Lancaster, Peter. Lambda-matrices and vibrating systems , Pergamon Press, 1966. xiii+196. Print.
• Lancaster, Peter. Lambda-matrices and vibrating systems (1966 and 2002). Pergamon. Dover Publications Inc., 1966. xx+193. Print.

Journal Article

• Freitas, P. and Lancaster, Peter. "On the optimal spectral abscissa for a system of linear oscillators.". SIAM Journal of Matrix Analysis and Applications 21. (2010): 195-208. Print.
• Lancaster, Peter and Tisseur, F.. "Hermitian quadratic matrix polynomials: solvents and inverse problems.". Linear Algebra and its Applications (to appear), Print.
• Boulton, L. and Lancaster, Peter. "Schur decomposition of a matrix and the boundary of the pseudospectrum.". SIAM J. Matrix Anal. and Appl.. (to appear), Print.
• Lancaster, Peter and Zaballa, I.. "A review of canonical forms for selfadjoint matrix polynomials.". Operator Theory: Advances and Applications (to appear), Print.
• Lancaster, Peter and Zaballa, I.. "Parametrizing structure preserving transformations of matrix polynomials.". Operator Theory: Advances and Applications (to appear), Print.
• Amiraslani, A., Corless, Rob, Lancaster, Peter and Amiraslani, Amirhossein. "Linearization of matrix polynomials expressed in polynomial bases". IMA Journal of Numerical Analysis, (2009). Print.
• Lancaster, Peter and Zaballa, I.. "Diagonalizable quadratic eigenvalue problems.". Mech. Systems and Signal Processing. 23. (2009): 141-157. Print.
• Amiraslani, A. and Lancaster, Peter. "Rayleigh quotient algorithms for nonsymmetric matrix pencils.". Numerical Algorithms. 51. (2009): 5-22. Print.
• Lancaster, Peter. "Model updating for self-adjoint quadratic eigenvalue problems.". Linear Algebra and its Applications 428. (2008): 2778-2790. Print.
• Lancaster, Peter. "Linearization of regular matrix polynomials". Electronic Journal of Linear Algebra 17. (2008): 21-27. Print.
• Boulton, L., Lancaster, Peter and Psarrakos, P.. "On pseudospecrta of matrix polynomials and their boundaries.". Math. of Computation 77. (2008): 313-334. Print.
• Lancaster, Peter. "Inverse spectral problems for semi-simple damped vibrating systems.". SIAM J. Matrix Anal. and Appl.. 29. (2007): 302-327. Print.
• Lancaster, Peter and Prells, U.. "Isospectral families of high-order systems". Z. Angew. Math. Mech.. 87. (2007): 219-234. Print.
• Lancaster, Peter, Prells, U. and Rodman, L.. "Canonical structures for palindromic matrix polynomials". Operators and Matrices 1. (2007): 469-489. Print.
• Wu, J-W.,, Lian, K-Y., and Lancaster, Peter. "A stabilization criterion for matrices.". Linear Algebra and its Applications. 422. (2007): 22-28. Print.
• Bohl, E. and Lancaster, Peter. "Implementation of a Markov model for phylogenetic trees.". Journal of Theoretical Biology 239.3 (2006): 324-333. Print.
• Lancaster, Peter and Psarrakos, P.. "On the pseudospectra of matrix polynomials.". SIAM Journal of Matrix Analysis and Applications 27. (2005): 115-129. Print.
• Lancaster, Peter and Rodman, L.. "Canonical forms for symmetric/skewsymsmetric real matrix pairs under strict equivalence and congruence.". Linear Algebra and its Applications 406. (2005): 1-76. Print.
• Guo, Chun-Hua and Lancaster, Peter. "Algorithms for hyperbolic quadratic eigenvalue problems.". Mathematics of Computation 74. (2005): 1777-1791. Print.
• Prells, U. and Lancaster, Peter. "Isospectral vibrating systems. Part II: Structure preserving transformations.". Operator Theory: Advances and Applications 163. (2005): 275-298. Print.
• Lancaster, Peter. "Isospectral vibrating systems. Part I: The spectral method.". Linear Algebra and its Applications. 409. (2005): 51-69. Print.
• Lancaster, Peter and Rodman, L.. "Canonical forms for hermitian matrix pairs under strict equivalence and congruence.". SIAM Review. 47. (2005): 407-443. Print.
• Lancaster, Peter and Prells, U.. "Inverse problems for damped vibrating systems.". Journal of Sound and Vibration 283. (2005): 891-914. Print.
• Farkas, A., Lancaster, Peter and Rozsa, P.. "Approximation of positive matrices by transitive matrices.". Computers and Mathematics with Applications 50. (2005): 1033-1039. Print.
• Lancaster, Peter and Psarrakos, P.. "Normal and seminormal eigenvalues of matrix functions.". Integral Equations and Operator Theory 41. (2003): 331-342. Print.
• Lancaster, Peter, Markus, A. S. and Zhou, F.. "Perturbation theory for analytic matrix functions: the semisimple case.". SIAM Journal of Matrix Analysis and Applications 25. (2003): 606-626. Print.
• Lancaster, Peter and Zhou, Fei. "A wider class of stable gyroscopic systems". Linear Algebra and its Applications 370. (2003): 257-267. Print.
• Farkas, Andr, Lancaster, Peter and R{\'o}zsa, P. "Consistency adjustments for pairwise comparison matrices". Numerical Linear Algebra with Applications 10.8 (2003): 689-700. Print.
• Bohl, Erich and Lancaster, Peter. "Irreversible Markov processes for phylogenetic models". Numerical Linear Algebra with Applications 10.7 (2003): 577-593. Print.
• Lancaster, Peter, Markus, A.S. and Psarrakos, P.. "Repeated eigenvectors and the numerical range of self-adjoint quadratic operator polynomials". Integral Equations and Operator Theory 44.2 Dover Publications Inc., (2002): 243-253. Print.
• Lancaster, Peter and Psarrakos, P.. "The numerical range of self-adjoint quadratic matrix polynomials". SIAM Journal on Matrix Analysis and Applications 23.3 Birkhauser, (2002): 615-631. Print.
• Lancaster, Peter. "Stabilization of gyroscopic systems". ZAMM. Zeitschrift f\"ur Angewandte Mathematik und Mechanik. Journal of Applied Mathematics and Mechanics 81.10 Birkhauser, (2001): 675-681. Print.
• Lancaster, Peter. "Normal and seminormal eigenvalues of matrix functions". Integral Equations and Operator Theory 41.3 Birkhauser, (2001): 331-342. Print.
• Lancaster, Peter and Markus, A.S.. "A note on factorization of analytic matrix functions.". Operator Theory: Advances and Applications 122. (2001): 323-330. Print.
• Kliem, W., Lancaster, Peter and Pommer, C.. "A precise bound for gyroscopic stabilization". ZAMM. Zeitschrift f\"ur Angewandte Mathematik und Mechanik. Journal of Applied Mathematics and Mechanics 80.8 Birkhauser, (2000): 507-516. Print.
• Dai, Hua and Lancaster, Peter. "Preconditioning block {L}anczos algorithm for solving symmetric eigenvalue problems". Journal of Computational Mathematics. An International Journal on Numerical Methods, Analysis and Applications 18.4 Birkhauser, (2000): 365-374. Print.
• Lancaster, Peter and Kliem, W.. "Comments on stability properties of conservative gyroscopic systems". American Society of Mechanical Engineers. Transactions of the ASME. Journal of Applied Mechanics 66.1 Birkhauser, (1999): 272-273. Print.
• Lancaster, Peter and Renshaw, A. A.. "A stability criterion for parameter-dependent gyroscopic systems". American Society of Mechanical Engineers. Transactions of the ASME. Journal of Applied Mechanics 66.3 Birkhauser, (1999): 660-664. Print.
• Freitas, Pedro and Lancaster, Peter. "On the optimal value of the spectral abscissa for a system of linear oscillators". SIAM Journal on Matrix Analysis and Applications 21.1 Birkhauser, (1999): 195-208 (electronic). Print.
• Guo, Chun and Lancaster, Peter. "Iterative solution of two matrix equations". Mathematics of Computation 68.228 Birkhauser, (1999): 1589-1603. Print.
• Lancaster, Peter. "Strongly stable gyroscopic systems". Electronic Journal of Linear Algebra 5. Birkhauser, (1999): 53-66 (electronic). Print.
• Lancaster, Peter. "On the perturbation of analytic matrix functions". Integral Equations and Operator Theory 34.3 Birkhauser, (1999): 325-338. Print.
• Lancaster, Peter and Zizler, Peter. "On the stability of gyroscopic systems". American Society of Mechanical Engineers. Transactions of the ASME. Journal of Applied Mechanics 65.2 Birkhauser, (1998): 519-522. Print.
• Krupnik, Ilya and Lancaster, Peter. "Linearization, realization, and scalar products for regular matrix polynomials". Linear Algebra and its Applications 272. Birkhauser, (1998): 45-57. Print.
• Krupnik, Ilya and Lancaster, Peter. "{$H$}-selfadjoint and {$H$}-unitary matrix pencils". SIAM Journal on Matrix Analysis and Applications 19.2 Birkhauser, (1998): 307-324 (electronic). Print.
• Krupnik, Ilya and Lancaster, Peter. "Minimal pencil realizations of rational matrix functions with symmetries". Canadian Mathematical Bulletin. Bulletin Canadien de Math\'ematiques 41.2 Birkhauser, (1998): 178-186. Print.
• Guo, Chun and Lancaster, Peter. "Analysis and modification of {N}ewton's method for algebraic {R}iccati equations". Mathematics of Computation 67.223 Birkhauser, (1998): 1089-1105. Print.
• Lancaster, Peter and Zizler, Peter. "The order of neutrality for linear operators on inner product spaces". Linear Algebra and its Applications 259. Birkhauser, (1997): 25-29. Print.
• Dai, Hua and Lancaster, Peter. "Newton's method for a generalized inverse eigenvalue problem". Numerical Linear Algebra with Applications 4.1 Birkhauser, (1997): 1-21. Print.
• Dai, Hua and Lancaster, Peter. "Numerical methods for finding multiple eigenvalues of matrices depending on parameters". Numerische Mathematik 76.2 Birkhauser, (1997): 189-208. Print.
• Hua, Dai and Lancaster, Peter. "Linear matrix equations from an inverse problem of vibration theory". Linear Algebra and its Applications 246. John Wiley & Sons Inc., (1996): 31-47. Print.
• Lancaster, Peter and Matsaev, V.. "Factorization of selfadjoint operator polynomials". Journal of Operator Theory 35.2 John Wiley & Sons Inc., (1996): 337-348. Print.
• Lancaster, Peter and R{\'o}zsa, P.. "The spectrum and stability of a vibrating rail supported by sleepers". Computers & Mathematics with Applications. An International Journal 31.4-5 Birkhauser, (1996): 201-213. Print.
• Krupnik, Ilya, Lancaster, Peter and Zizler, Peter. "Factorization of selfadjoint matrix polynomials with real spectrum". Linear and Multilinear Algebra 40.4 Birkhauser, (1996): 327-336. Print.
• Lancaster, Peter and Rodman, L.. "Minimal symmetric factorizations of symmetric real and complex rational matrix functions". Linear Algebra and its Applications 220. The Clarendon Press Oxford University Press, (1995): 249-282. Print.
• Krupnik, Ilya and Lancaster, Peter. "Factorization of selfadjoint quadratic matrix polynomials with real spectrum". Linear and Multilinear Algebra 39.3 The Clarendon Press Oxford University Press, (1995): 263-272. Print.
• Andrew, A. L., Chu, K. E. and Lancaster, Peter. "On the numerical solution of nonlinear eigenvalue problems". Computing. Archives for Scientific Computing 55.2 The Clarendon Press Oxford University Press, (1995): 91-111. Print.
• Lancaster, Peter and Matsaev, V. I.. "Definitizable operators and quasihyperbolic operator polynomials". Journal of Functional Analysis 131.1 The Clarendon Press Oxford University Press, (1995): 1-28. Print.
• Lancaster, Peter and Ye, Qiang. "Low rank perturbations of strongly definitizable transformations and matrix polynomials". Linear Algebra and its Applications 197/198. The Clarendon Press Oxford University Press, (1994): 3-29. Print.
• Lancaster, Peter and Rodman, L.. "Invariant neutral subspaces for symmetric and skew real matrix pairs". Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 46.3 The Clarendon Press Oxford University Press, (1994): 602-618. Print.
• Lancaster, Peter and Shkalikov, A.. "Damped vibrations of beams and related spectral problems". The Canadian Applied Mathematics Quarterly 2.1 The Clarendon Press Oxford University Press, (1994): 45-90. Print.
• Lancaster, Peter, Shkalikov, A. and Ye, Qiang. "Strongly definitizable linear pencils in {H}ilbert space". Integral Equations and Operator Theory 17.3 The Clarendon Press Oxford University Press, (1993): 338-360. Print.
• Lancaster, Peter and Ye, Qiang. "Definitizable {H}ermitian matrix pencils". Aequationes Mathematicae 46.1-2 (1993): 44-55. Print.
• Lancaster, Peter and Ye, Qiang. "Rayleigh-{R}itz and {L}anczos methods for symmetric matrix pencils". Linear Algebra and its Applications 185. (1993): 173-201. Print.
• Bohl, Erich and Lancaster, Peter. "Perturbation of spectral inverses applied to a boundary layer phenomenon arising in chemical networks". Linear Algebra and its Applications 180. (1993): 35-59. Print.
• Andrew, Alan L., Chu, K. and Lancaster, Peter. "Derivatives of eigenvalues and eigenvectors of matrix functions". SIAM Journal on Matrix Analysis and Applications 14.4 The Clarendon Press Oxford University Press, (1993): 903-926. Print.
• Gohberg, I., Koltracht, I. and Lancaster, Peter. "Second order parallel algorithms for piecewise smooth displacement kernels". Integral Equations and Operator Theory 15.1 (1992): 16-29. Print.
• Barkwell, Lawrence and Lancaster, Peter. "Overdamped and gyroscopic vibrating systems". American Society of Mechanical Engineers. Transactions of the ASME. Journal of Applied Mechanics 59.1 (1992): 176-181. Print.
• Jameson, Antony, Kreindler, Eliezer and Lancaster, Peter. "Symmetric, positive semidefinite, and positive definite real solutions of {$AX=XA\sp {\ssf T}$} and {$AX=YB$}". Linear Algebra and its Applications 160. (1992): 189-215. Print.
• Barkwell, Lawrence and Lancaster, Peter. "Gyroscopically stabilized systems: a class of quadratic eigenvalue problems with real spectrum". Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 44.1 (1992): 42-53. Print.
• Andrew, Alan L., Chu, K. and Lancaster, Peter. "Sensitivities of eigenvalues and eigenvectors of problems nonlinear in the eigenparameter". Applied Mathematics Letters. An International Journal of Rapid Publication 5.3 (1992): 69-72. Print.
• Farid, F. O. and Lancaster, Peter. "Spectral Properties of Diagonally Dominant Infinite Matrices. II". Linear Algebra and its Applications 143. Springer, (1991): 7-17. Print.
• Bruckstein, Alfred, Kailath, Thomas, Koltracht, Israel and Lancaster, Peter. "On the reconstruction of layered media from reflection data". SIAM Journal on Matrix Analysis and Applications 12.1 Springer, (1991): 24-40. Print.
• Lancaster, Peter and Ye, Qiang. "Variational and numerical methods for symmetric matrix pencils". Bulletin of the Australian Mathematical Society 43.1 Springer, (1991): 1-17. Print.
• Elsner, L., Koltracht, I. and Lancaster, Peter. "Convergence properties of {ART} and {SOR} algorithms". Numerische Mathematik 59.1 Springer, (1991): 91-106. Print.
• Koltracht, Israel, Lancaster, Peter and Smith, Digby. "The structure of some matrices arising in tomography". Linear Algebra and its Applications 130. Springer, (1990): 193-218. Print.
• Koltracht, I. and Lancaster, Peter. "Constraining strategies for linear iterative processes". IMA Journal of Numerical Analysis 10.4 Springer, (1990): 555-567. Print.
• Gohberg, I., Koltracht, I. and Lancaster, Peter. "On the numerical solution of integral equations with piecewise continuous displacement kernels". Integral Equations and Operator Theory 12.4 Birkhauser, (1989): 511-538. Print.
• Farid, F. O. and Lancaster, Peter. "Spectral Properties of Diagonally Dominant Infinite Matrices, Part I.". Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 111A.3-4 Birkhauser, (1989): 301-314. Print.
• Gohberg, I., Kaashoek, M. A. and Lancaster, Peter. "General theory of regular matrix polynomials and band {T}oeplitz operators". Integral Equations and Operator Theory 11.6 Birkhauser, (1988): 776-882. Print.
• Lancaster, Peter and Ye, Qiang. "Inverse spectral problems for linear and quadratic matrix pencils". Linear Algebra and its Applications 107. Birkhauser, (1988): 293-309. Print.
• Koltracht, I. and Lancaster, Peter. "Generalized {S}chur parameters and the effects of perturbations". Linear Algebra and its Applications 105. Birkhauser, (1988): 109-129. Print.
• Lancaster, Peter and Maroulas, J.. "Selective perturbation of spectral properties of vibrating systems using feedback". Linear Algebra and its Applications 98. Birkhauser, (1988): 309-330. Print.
• Gohberg, I., Koltracht, I. and Lancaster, Peter. "Second order parallel algorithms for {F}redholm integral equations with continuous displacement kernels". Integral Equations and Operator Theory 10.4 Birkhauser, (1987): 577-594. Print.
• Lancaster, Peter and Maroulas, J.. "Inverse eigenvalue problems for damped vibrating systems". Journal of Mathematical Analysis and Applications 123.1 Birkhauser, (1987): 238-261. Print.
• Lancaster, Peter. "Alexander {M}. {O}strowski, 1893-1986". Aequationes Mathematicae 33.2-3 Birkhauser, (1987): 121-122. Print.
• Gohberg, I., Kailath, T., Koltracht, I. and Lancaster, Peter. "Linear complexity parallel algorithms for linear systems of equations with recursive structure". Linear Algebra and its Applications 88/89. Birkhauser, (1987): 271-315. Print.
• Lancaster, Peter, Ran, A. C. M. and Rodman, L.. "An existence and monotonicity theorem for the discrete algebraic matrix {R}iccati equation". Linear and Multilinear Algebra 20.4 Birkhauser, (1987): 353-361. Print.
• Koltracht, I. and Lancaster, Peter. "A definiteness test for {H}ankel matrices and their lower submatrices". Computing. Archives for Scientific Computing 39.1 Birkhauser, (1987): 19-26. Print.
• Lancaster, Peter. "Common eigenvalues, divisors, and multiples of matrix polynomials: a review". Linear Algebra and its Applications 84. John Wiley & Sons Inc., (1986): 139-160. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. "On {H}ermitian solutions of the symmetric algebraic {R}iccati equation". SIAM Journal on Control and Optimization 24.6 John Wiley & Sons Inc., (1986): 1323-1334. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. "Quadratic matrix polynomials with a parameter". Advances in Applied Mathematics 7.3 John Wiley & Sons Inc., (1986): 253-281. Print.
• Lancaster, Peter, Ran, A. C. M. and Rodman, L.. "Hermitian solutions of the discrete algebraic {R}iccati equation". International Journal of Control 44.3 John Wiley & Sons Inc., (1986): 777-802. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. "Perturbation of analytic {H}ermitian matrix functions". Applicable Analysis. An International Journal 20.1-2 John Wiley & Sons Inc., (1985): 23-48. Print.
• Elsner, L. and Lancaster, Peter. "The spectral variation of pencils of matrices". Journal of Computational Mathematics. An International Journal on Numerical Methods, Analysis and Applications 3.3 John Wiley & Sons Inc., (1985): 262-274. Print.
• Lancaster, Peter and Maroulas, J.. "The kernel of the {B}ezoutian for operator polynomials". Linear and Multilinear Algebra 17.3-4 John Wiley & Sons Inc., (1985): 181-201. Print.
• Lancaster, Peter, Lerer, L. and Tismenetsky, M.. "Factored forms for solutions of {$AX-XB=C$} and {$X-AXB=C$} in companion matrices". Linear Algebra and its Applications 62. Springer, (1984): 19-49. Print.
• Lancaster, Peter and R{\'o}zsa, P.. "Eigenvectors of {$H$}-selfadjoint matrices". Zeitschrift f\"ur Angewandte Mathematik und Mechanik. Ingenieurwissenschaftliche Forschungsarbeiten 64.9 Springer, (1984): 439-441. Print.
• Gohberg, Israel, Lancaster, Peter and Rodman, Leiba. "A sign characteristic for selfadjoint meromorphic matrix functions". Applicable Analysis. An International Journal 16.3 Birkhauser Verlag, (1983): 165-185. Print.
• Lancaster, Peter and Tismenetsky, M.. "Inertia characteristics of selfadjoint matrix polynomials". Linear Algebra and its Applications 52/53. Birkhauser Verlag, (1983): 479-496. Print.
• Lancaster, Peter and R{\'o}zsa, P.. "On the matrix equation {$AX+X\sp{\ast} A\sp{\ast} =C$}". Society for Industrial and Applied Mathematics. Journal on Algebraic and Discrete Methods 4.4 Birkhauser Verlag, (1983): 432-436. Print.
• Lancaster, Peter and Tismenetsky, M.. "Some extensions and modifications of classical stability tests for polynomials". International Journal of Control 38.2 Birkhauser Verlag, (1983): 369-380. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. "Perturbations of {$H$}-selfadjoint matrices, with applications to differential equations". Integral Equations and Operator Theory 5.5 Hemisphere, (1982): 718-757. Print.
• Lancaster, Peter and Pattabhiraman, M. V.. "The local determination of {J}ordan bases for {$H$}-selfadjoint operators". Linear Algebra and its Applications 48. Dekker, (1982): 191-199. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. "Factorization of selfadjoint matrix polynomials with constant signature". Linear and Multilinear Algebra 11.3 Academic Press Inc. [Harcourt Brace Jovanovich Publishers], (1982): 209-224. Print.
• Lancaster, Peter and Salkauskas, Kes. "Surfaces generated by moving least squares methods". Mathematics of Computation 37.155 Academic Press Inc. [Harcourt Brace Jovanovich Publishers], (1981): 141-158. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. "Spectral analysis of selfadjoint matrix polynomials". Annals of Mathematics. Second Series 112.1 Academic Press Inc. [Harcourt Brace Jovanovich Publishers], (1980): 33-71. Print.
• Barnett, S. and Lancaster, Peter. "Some properties of the {B}ezoutian for polynomial matrices". Linear and Multilinear Algebra 9.2 Academic Press Inc. [Harcourt Brace Jovanovich Publishers], (1980): 99-110. Print.
• Lancaster, Peter and Rodman, L.. "Existence and uniqueness theorems for the algebraic {R}iccati equation". International Journal of Control 32.2 Academic Press Inc. [Harcourt Brace Jovanovich Publishers], (1980): 285-309. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. "On selfadjoint matrix polynomials". Integral Equations and Operator Theory 2.3 Academic Press Inc. [Harcourt Brace Jovanovich Publishers], (1979): 434-439. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. "Perturbation theory for divisors of operator polynomials". SIAM Journal on Mathematical Analysis 10.6 Academic Press Inc. [Harcourt Brace Jovanovich Publishers], (1979): 1161-1183. Print.
• Lancaster, Peter. "Solving quadratic equations". Menemui Matematik. (Discovering Mathematics) 1.3 Academic Press Inc. [Harcourt Brace Jovanovich Publishers], (1979): 23-36. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. "Representations and divisibility of operator polynomials". Canadian Journal of Mathematics. Journal Canadien de Math\'ematiques 30.5 (1978): 1045-1069. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. "Spectral analysis of matrix polynomials. {I}. {C}anonical forms and divisors". Linear Algebra and Appl. 20.1 (1978): 1-44. Print.
• Gohberg, I., Lancaster, Peter and Rodman, L.. "Spectral analysis of matrix polynomials. {II}. {T}he resolvent form and spectral divisors". Linear Algebra and Appl. 21.1 (1978): 65-88. Print.
• Lancaster, Peter and Rokne, Jon G.. "Solutions of nonlinear operator equations". SIAM Journal on Mathematical Analysis 8.3 Birkhauser, (1977): 448-457. Print.
• Terray, J. and Lancaster, Peter. "On the numerical calculation of eigenvalues and eigenvectors of operator polynomials". J. Math. Anal. Appl. 60.2 (1977): 370-378. Print.
• Lancaster, Peter. "A fundamental theorem on lambda-matrices with applications. {II}. {D}ifference equations with constant coefficients". Linear Algebra and Appl. 18.3 Birkhauser, (1977): 213-222. Print.
• Lancaster, Peter. "A fundamental theorem on lambda-matrices with applications. {I}. {O}rdinary differential equations with constant coefficients". Linear Algebra and Appl. 18.3 Birkhauser, (1977): 189-211. Print.
• Watkins, D. S. and Lancaster, Peter. "Some families of finite elements". J. Inst. Math. Appl. 19.4 Birkhauser, (1977): 385-397. Print.
• Lancaster, Peter. "Interpolation in a rectangle and finite elements of high degree". J. Inst. Math. Appl. 18.1 Birkhauser, (1976): 67-77. Print.
• Lancaster, Peter and Wimmer, Harald K.. "Zur {T}heorie der {$\lambda $}-{M}atrizen". Mathematische Nachrichten 68. Birkhauser, (1975): 325-330. Print.
• Schmidt, Eckard, Lancaster, Peter and Watkins, David. "Bases of splines associated with constant coefficient differential operators". SIAM Journal on Numerical Analysis 12.4 Birkhauser, (1975): 630-645. Print.
• Cross, G. W. and Lancaster, Peter. "Square roots of complex matrices". Linear and Multilinear Algebra 1. Birkhauser, (1973/74): 289-293. Print.
• Lancaster, Peter and Farahat, Hanafi K.. "Norms on direct sums and tensor products". Mathematics of Computation 26. Birkhauser, (1972): 401-414. Print.
• Lancaster, Peter. "A note on sub-multiplicative norms". Numerische Mathematik 19. Birkhauser, (1972): 206-208. Print.
• Schmidt, Eckard and Lancaster, Peter. "{$L$}-splines for constant coefficient differential operators". , Birkhauser, (1971): 457-462. Print.
• Lancaster, Peter. "Some questions in the classical theory of vibrating systems". Bul. Inst. Politehn. Ia\c si (N.S.) 17(21).1-2, part 1 Birkhauser, (1971): 125-132. Print.
• Lancaster, Peter. "Jordan chains for lambda matrices. {II}". Aequationes Mathematicae 5. Birkhauser, (1970): 290-293. Print.
• Lancaster, Peter. "Explicit solutions of linear matrix equations". SIAM Review. A Publication of the Society for Industrial and Applied Mathematics 12. Birkhauser, (1970): 544-566. Print.
• Pattabhiraman, M. V. and Lancaster, Peter. "Spectral properties of a polynomial operator". Numerische Mathematik 13. Birkhauser, (1969): 247-259. Print.
• Rokne, J. and Lancaster, Peter. "Automatic errorbounds for the approximate solution of equations". Computing (Arch. Elektron. Rechnen) 4. Birkhauser, (1969): 294-303. Print.
• Lancaster, Peter and Webber, P. N.. "Jordan chains for lambda matrices". Linear Algebra and Appl. 1. Academic Press, (1968): 563-569. Print.
• Lancaster, Peter. "Error analysis for the {N}ewton-{R}aphson method". Numerische Mathematik 9. Academic Press, (1966): 55-68. Print.
• Lancaster, Peter. "Convergence of the {N}ewton-{R}aphson method for arbitrary polynomials". Math. Gaz. 48. Academic Press, (1964): 291-295. Print.
• Lancaster, Peter. "Bounds for latent roots in damped vibration problems". SIAM Review. A Publication of the Society for Industrial and Applied Mathematics 6. Academic Press, (1964): 121-125. Print.
• Lancaster, Peter. "On eigenvalues of matrices dependent on a parameter". Numerische Mathematik 6. Academic Press, (1964): 377-387. Print.
• Lancaster, Peter. "Algorithms for lambda-matrices". Numerische Mathematik 6. Academic Press, (1964): 388-394. Print.
• Lancaster, Peter. "Some applications of the {N}ewton-{R}aphson method to non-linear matrix problems". Proc. Roy. Soc. Ser. A 271. (1963): 324-331. Print.
• Lancaster, Peter. "On regular pencils of matrices arising in the theory of vibrations". Quart. J. Mech. Appl. Math. 16. (1963): 253-257. Print.
• Lancaster, Peter. "A generalized {R}ayleigh quotient iteration for lambda-matrices". Archive for Rational Mechanics and Analysis 8. (1961): 309-322. Print.
• Lancaster, Peter. "Free vibrations of lightly damped systems by perturbations methods.". Quart. J. Mech. Appl. Math. 13. (1960): 138-155. Print.
• Lancaster, Peter. "Inversion of lambda-matrices and application to the theory of linear vibrations". Archive for Rational Mechanics and Analysis 6. (1960): 105-114. Print.

Preprint

• Lancaster, Peter. "Lectures on Linear Algebra, Control, and Stability". , (1998). Print.