SIAM AG on Orthogonal Polynomials and Special Functions


Extract from OP-SF NET

Topic #11  ------------   OP-SF NET 4.5  ------------ September 15, 1997
From: OP-SF NET Editor (
Subject: Rivlin Festschrift

Annals of Numerical Mathematics Vol 4, 1997 is a special issue on "The
heritage of P.L. Chebyshev: A Festschrift in honor of the 70th birthday of
T.J. Rivlin".  This special issue is edited by Charles A. Micchelli.  The
following table of contents is found at the URL: .
A considerable part of the included papers deals with orthogonal

Charles A. Micchelli

On the work of Theodore J. Rivlin
C.A. Micchelli

A brief preface
T.J. Rivlin

On Chebyshev polynomials in dynamics
R. Adler, B. Kitchens, C.A. Micchelli and C. Tresser 1

Renewal sequences and ordered partitions
J.M. Anderson and A. Hinkkanen 11

Bounds for the trace of the inverse and the determinant of symmetric
positive definite matrices
Z. Bai and G.H. Golub 29

On approximation by exponentials
B.J.C. Baxter and A. Iserles 39

A discrepancy lemma for oscillating polynomials and sign changes of the
error function of best approximants
H.-P. Blatt 55 

On the zeros of various kinds of orthogonal polynomials
C. Brezinski and M. Redivo-Zaglia 67

On the lower semicontinuity of best rational Chebyshev approximation
B. Brosowski 79

Rivlin's problem
B. Brosowski and F. Deutsch 95

Lebesgue functions for polynomial interpolation -- a survey
L. Brutman 111

On a recovery problem
M. Buhmann and A. Pinkus 129

The approximate sampling theorem, Poisson's sum formula, a decomposition
theorem for Parseval's equation and their interconnections
P.L. Butzer and A. Gessinger 143

Support and foundation of bases
J.M. Carnicer, T.N.T. Goodman and J.M. Pen¬a 161

Lacunary interpolation by cosine polynomials
A.S. Cavaretta, C.R. Selvaraj and A. Sharma 181

A study of asymptotically optimal time-frequency localization by scaling
functions and wavelets
C.K. Chui and J.Z. Wang 193
A de Montessus theorem for multivariate homogeneous Padé approximants
A. Cuyt and D.S. Lubinsky 217

The multiplicity of a spline zero
C. de Boor 229

Overconvergence of some simultaneous Hermite-Padé interpolants
M.G. de Bruin and A. Sharma 239

Approximation by feed-forward neural networks
R.A. DeVore, K.I. Oskolkov and P.P. Petrushev 261

Uniqueness of least-norm generalized monosplines induced by log-concave
N. Dyn 289

On upper bounds for the number of extrema of Chebyshev alternants
M.K. El-Daou and E.L. Ortiz 301

Polynomial approximation of functions continuous on [-1, 1] and analytic
on (-1, 1)
D. Gaier 315

On the computation of special Sobolev-type orthogonal polynomials
W. Gautschi 329

On some recursive triangular systems
W.M.Y. Goh, E. Schmutz and J. Wimp 343

On a measure of dissimilarity between positive definite matrices
A.J. Hoffman and C.A. Micchelli 351

On computing Ax and pi^T A, when A is sparse
A.J. Hoffman, W.R. Pulleyblank and J.A. Tomlin 359

The dynamics of group automorphisms
B. Kitchens 369

A variational approach to optimizing linear functionals over Haar spaces
A. Kroo and D. Schmidt 393

Weighted polynomial approximation of some entire functions on the real
A. Kroo, J. Szabados and R.S. Varga 405

On monotone and convex approximation by splines with free knots
D. Leviatan and A. Shadrin 415

On optimal Pade-type cuts
A.P. Magnus 435

Subdivision schemes with non-negative masks converge always -- unless they
obviously cannot?
A.A. Melkman 451

On a measure of dissimilarity for normal probability densities
C.A. Micchelli 461

A splitting problem
D.J. Newman 479

Fast multipoint polynomial evaluation and interpolation via computations
with structured matrices 
V.Y. Pan, A. Zheng, X. Huang and Y. Yu 483

Bernstein polynomials based on the q-integers
G.M. Phillips 511

A new iterative algorithm for thin plate spline interpolation in two
M.J.D. Powell 519

The Fundamental Theorem of Linear Programming applied to certain extremal
problems for polynomials
M.A. Qazi and Q.I. Rahman 529

Optimal recovery in translation-invariant spaces of functions
R. Schaback 547

The Chebyshev constant of a linear set
H.S. Shapiro 557

On the zeros of generalized Jacobi polynomials
P. Vertesi 561

Smoothing spline ANOVA fits for very large, nearly regular data sets, with
application to historical global climate data
G. Wahba and Z. Luo 579

Measurable entire functions
B. Weiss 599

Strong tractability of weighted tensor products
H. Wozniakowski 607

Summability of certain product ultraspherical orthogonal series in several
Y. Xu 623

Author index 639

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