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Len Bos

photograph of Len Bos

Job Title:

  • Professor

Phone:

  • +1 (403) 220-3937

Office:

  • MS 584

Degrees:

Research Interests:

  • Markovs inequality on sets with cusps and its relation to other phenomenon such as Sobolev-type inequalities and the extension of C (infinity) functions
  • Tangential Markov/Bernstein inequalities on manifolds
  • Weighted splines and minimum norm networks

Ph. D. Student:

  • Gergely (Greg) Orosi (2009)

Masters Students:

  • Aaron Pratt (2008)
  • Paul Wong (2005)

Past Courses:

  • AMAT001 - MODULE M1
  • AMAT002 - MODULE M2
  • AMAT217 - CALCULUS FOR ENGINEER & SCIENTIST
  • AMAT219 - MULTIVARIABLE CALC FOR ENGINEERS
  • AMAT307 - DIFFERENTIAL EQUATION ENGINEERS
  • AMAT309 - VECTOR CALCULUS FOR ENGINEERS
  • AMAT371 - COMPUTING FOR MATHEMATICIANS
  • AMAT413 - INTRO TO PARTIAL DIFF EQUATIONS
  • AMAT415 - MATHEMATICAL METHODS
  • AMAT481 - INTRO TO MATHEMATICAL FINANCE
  • AMAT483 - COMPUTATIONAL METHODS MATH FNCE
  • AMAT491 - NUMERICAL ANALYSIS
  • AMAT671 - NUMERICAL LINEAR ALGEBRA
  • AMAT673 - APPROXIMATION THEORY
  • MATH032 - Introduction to Mathematical Software
  • MATH253 - CALCULUS II
  • MATH263 - Enriched Calculus II
  • PMAT501 - INTEGRATION THEORY
Representative Publications:
Journal Paper
Bos, Len, Brudnyi, Alex, Levenberg, N. and Totik, V. . "Tangential Markov inequalities on transcendental curves" Constructive Approximation. An International Journal for Approximations and Expansions 19.3 (2003): 339-354
Bos, Len and Maier, U. . "On the asymptotics of {F}ekete-type points for univariate radial basis interpolation" Journal of Approximation Theory 119.2 (2002): 252-270
Bos, Len, Ware, Antony and Pavlov, B. S. "On a semi-spectral method for pricing an option on a mean-reverting asset" Quantitative Finance 2.5 (2002): 337-345
Bagby, T. , Bos, Len and Levenberg, N. . "Multivariate simultaneous approximation" Constructive Approximation. An International Journal for Approximations and Expansions 18.4 (2002): 569-577
Bos, Len and Marchi, Stefano . "On the limit under scaling of polynomial {L}agrange interpolation on analytic manifolds" Rendiconti del Circolo Matematico di Palermo. Serie II. Supplemento68, part I (2002): 303-314
Bos, Len, Calvi, Jean and Levenberg, Norman . "On the {S}iciak extremal function for real compact convex sets" Arkiv f\"or Matematik 39.2 (2001): 245-262
Bos, Len, Taylor, M. A. and Wingate, B. A. "Tensor product {G}auss-{L}obatto points are {F}ekete points for the cube" Mathematics of Computation 70.236 (2001): 1543-1547 (electronic)
Bos, Len and Marchi, Stefano . "Fekete points for bivariate polynomials restricted to {$y=x\sp m$}" East Journal on Approximations 6.2 (2000): 189-200
Bos, Len and Marchi, S. . "Limiting values under scaling of the {L}ebesgue function for polynomial interpolation on spheres" Journal of Approximation Theory 96.2 (1999): 366-377
Bos, Len, Levenberg, N. , Milman, P. D. and Taylor, B. A. "Tangential {M}arkov inequalities on real algebraic varieties" Indiana University Mathematics Journal 47.4 (1998): 1257-1272
Korevaar, J. and Bos, Len. "Characterization of algebraic curves by {C}hebyshev quadrature" Journal d'Analyse Math\'ematique 75 (1998): 233-246
Bos, Len, Vecchia, B. and Mastroianni, G. . "On the asymptotics of {C}hristoffel functions for centrally symmetric weight functions on the ball in {$\bold R\sp d$}" Rendiconti del Circolo Matematico di Palermo. Serie II. Supplemento52, Vol. I (1998): 277-290
Bos, Len and Calvi, Jean . "Kergin interpolants at the roots of unity approximate {$C\sp 2$} functions" Journal d'Analyse Math\'ematique 72 (1997): 203-221
Bos, Len and Holland, Darius. "Network splines" Results in Mathematics. Resultate der Mathematik 30.3-4 (1996): 228-258
Bos, Len, Grabenstetter, J. E. and Salkauskas, Kes . "Pseudo-tensor product interpolation and blending with families of univariate schemes" Computer Aided Geometric Design 13.5 (1996): 429-440
Bagby, Thomas , Bos, Len and Levenberg, Norman . "Quantitative approximation theorems for elliptic operators" Journal of Approximation Theory 85.1 (1996): 69-87
Bos, Len and Milman, P. D. "Sobolev-{G}agliardo-{N}irenberg and {M}arkov type inequalities on subanalytic domains" Geometric and Functional Analysis 5.6 (1995): 853-923
Bos, Len, Levenberg, N. , Milman, P. and Taylor, B. A. "Tangential {M}arkov inequalities characterize algebraic submanifolds of {${\bf R}\sp N$}" Indiana University Mathematics Journal 44.1 (1995): 115-138
Bos, Len. "Asymptotics for the {C}hristoffel function for {J}acobi like weights on a ball in {${\bf R}\sp m$}" New Zealand Journal of Mathematics 23.2 (1994): 99-109
Bos, Len and Salkauskas, Kes . "Limits of weighted splines based on piecewise constant weight functions" The Rocky Mountain Journal of Mathematics 23.2 (1993): 483-493
Salkauskas, Kes and Bos, Len. "Weighted splines as optimal interpolants" The Rocky Mountain Journal of Mathematics 22.2 (1992): 705-717
Bloom, T. , Bos, Len, Christensen, C. and Levenberg, N. . "Polynomial interpolation of holomorphic functions in {${\bf C}$} and {${\bf C}\sp n$}" The Rocky Mountain Journal of Mathematics 22.2 (1992): 441-470
Bos, Len. "On certain configurations of points in {${\bf R}\sp n$} which are unisolvent for polynomial interpolation" Journal of Approximation Theory 64.3 (1991): 271-280
Bos, Len. "Some remarks on the {F}ej\'er problem for {L}agrange interpolation in several variables" Journal of Approximation Theory 60.2 (1990): 133-140
Bos, Len and Salkauskas, Kes . "Moving least-squares are {B}ackus-{G}ilbert optimal" Journal of Approximation Theory 59.3 (1989): 267-275
Bos, Len. "A characteristic of points in {${\bf R}\sp 2$} having {L}ebesgue function of polynomial growth" Journal of Approximation Theory 56.3 (1989): 316-329
Bos, Len and Salkauskas, Kes . "Comment on the representation of splines as {B}oolean sums" Journal of Approximation Theory 53.2 (1988): 155-162
Bos, Len and Salkauskas, Kes . "On the matrix {$[\vert x\sb i-x\sb j\vert \sp 3]$} and the cubic spline continuity equations" Journal of Approximation Theory 51.1 (1987): 81-88
Gotay, Mark J. and Bos, Len. "Singular angular momentum mappings" Journal of Differential Geometry 24.2 (1986): 181-203
Bos, Len and Torrence, R. J. "Comment on the {L}iouville equation and multisolitons" Physics Letters. A 111.3 (1985): 95-96
Galler, Bruce I. and Bos, Len. "A model of transaction blocking in databases" Performance Evaluation. An International Journal 3.2 (1983): 95-122
Bos, Len. "Bounding the {L}ebesgue function for {L}agrange interpolation in a simplex" Journal of Approximation Theory 38.1 (1983): 43-59
Bos, Len. "On {K}ergin interpolation in the disk" Journal of Approximation Theory 37.3 (1983): 251-261
Book
Bos, Len and Waldron, Shayne . On the structure of {K}ergin interpolation for points in general position 137, Birkh\"auser (2001): 75-87
Bos, Len and Maier, Ulrike . On the asymptotics of points which maximize determinants of the form {$\det[g(\vert x\sb i-x\sb j\vert )]$} 107, Wiley-VCH, Berlin (1999): 107-128
Bos, Len and Pavlov, Boris . Absolute continuity of convolutions of singular measures and new branches of spectrum of {L}iouvillians and few-body {H}amiltonians 399, Chapman \& Hall/CRC, Boca Raton, FL (1999): 308-322
Bos, Len and Holland, Darius. Radial extensions of vertex data 18, Amer. Math. Soc. (1999): 5-14
Bos, Len, Levenberg, N. and Taylor, B. A. Characterization of smooth, compact algebraic curves in {${\bf R}\sp 2$} 31, Polish Acad. Sci. (1995): 125-134
Bos, Len and Milman, P. D. On {M}arkov and {S}obolev type inequalities on sets in {$\bold R\sp n$} World Sci. Publishing (1993): 81-100
Bos, Len and Salkauskas, Kes . Weighted splines based on piecewise polynomial weight functions , SIAM (1992): 87-98
Bos, Len and Milman, P. D. The equivalence of the usual and quotient topologies for {$C\sp \infty(E)$} when {$E\subset{\bf R}\sp n$} is {W}hitney {$p$}-regular 356, Kluwer Acad. Publ. (1992): 279-292
Bos, Len, Grabenstetter, J. E. and Salkauskas, Kes . Finite element interpolation with weighted smoothing 2, Acad. Cienc. Exact. F\'\i s. Qu\'\i m. Nat. Zaragoza (1990): 17-23
Bos, Len. Asymptotics for the {C}hristoffel function for the equilibrium measure on a ball in {${\bf R}\sp m$} Academic Press (1989): 97-100
Bos, Len and Gotay, Mark J. Reduced canonical formalism for a particle with zero angular momentum World Sci. Publishing (1984): 83-91
Bos, Len and Bloom, Thomas . On the convergence of {K}ergin interpolants of analytic functions Academic Press (1983): 369-374