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Title Walter Gautschi. Volume 1 : selected works with commentaries / edited by Claude Brezinski, Ahmed Sameh
Published New York : Birkhäuser, 2013
Table of Contents
 List of Contributorsxi
1.Preface1
pt. I Walter Gautschi 
2.Biography of Walter Gautschi / Ahmed Sameh5
3.A Brief Summary of My Scientific Work and Highlights of My Career / Walter Gautschi9
4.Publications / Walter Gautschi19
pt. II Commentaries 
5.Numerical Conditioning / Nicholas J. Higham37
5.1.Conditioning of Vandermonde Matrices37
5.2.Conditioning of Polynomials39
6.Special Functions / Javier Segura41
6.1.Computation of Special Functions42
6.1.1.Exponential Integrals, Incomplete Gamma Functions, and the Error Function42
6.1.2.Computing Special Functions by Gaussian Quadrature44
6.2.Inequalities45
6.2.1.Orthogonal Polynomials and Their Zeros45
6.2.2.Gamma Functions46
7.Interpolation and Approximation / Miodrag M. Spalevic49
7.1.Attenuation Factors in Practical Fourier Analysis49
7.2.Pade Approximants Associated with Hamburger Series50
7.3.Convergence Behavior of Continued Fractions with Real Elements51
7.4.Moment-preserving Spline Approximation52
7.5.Convergence of Extended Lagrange Interpolation53
7.6.Experimental Mathematics Involving Orthogonal Polynomials53
7.6.1.Jacobi Polynomials53
7.6.2.Quadrature Formulae54
7.7.Exotic Weight Functions54
pt. III Reprints 
8.Papers on Numerical Conditioning59
8.1.[16] On Inverses of Vandermonde and Confluent Vandermonde Matrices, Numer. Math. 4, 117--123 (1962)60
8.2.[19] On Inverses of Vandermonde and Confluent Vandermonde Matrices. II, Numer. Math. 5, 425--430 (1963)68
8.3.[43] The Condition of Orthogonal Polynomials, Math. Comp. 26, 923--924 (1972)75
8.4.[45] On the Condition of Algebraic Equations, Numer. Math. 21, 405--424 (1973)78
8.5.[51] Norm Estimates for Inverses of Vandermonde Matrices, Numer. Math. 23, 337--347 (1975)99
8.6.[62] On Inverses of Vandermonde and Confluent Vandermonde Matrices III, Numer. Math. 29, 445--450 (1978)111
8.7.[64] Questions of Numerical Condition Related to Polynomials, in Symposium on Recent Advances in Numerical Analysis (C. de Boor and G. H. Golub, eds.), 45--72 (1978) [Revised and reprinted in MAA Studies in Mathematics 24: Studies in Numerical Analysis (G. H. Golub, ed.), 140--177, Math. Assoc. America, Washington, DC, [ect.]118
8.8.[66] The Condition of Polynomials in Power Form, Math. Comp. 33, 343--352 (1979)157
8.9.[83] The Condition of Vandermonde-like Matrices Involving Orthogonal Polynomials, Linear Algebra Appl. 52/53, 293--300 (1983)168
8.10.[110] (with G. Inglese) Lower Bounds for the Condition Number of Vandermonde Matrices, Numer. Math. 52, 241--250 (1988)177
8.11.[118] How (Un)stable Are Vandermonde Systems?, in Asymptotic and Computational Analysis (R. Wong, ed.), 193--210, Lecture Notes Pure Appl. Math. 124 (1990)188
8.12.[120] (with A. Cordova and S. Ruscheweyh) Vandermonde Matrices on the Circle: Spectral Properties and Conditioning, Numer. Math. 57, 577--591 (1990)207
8.13.[200] Optimally Scaled and Optimally Conditioned Vandermonde and Vandermonde-like Matrices, BIT Numer. Math. 51, 103--125 (2011)223
9.Papers on Special Functions247
9.1.[9] Some Elementary Inequalities Relating to the Gamma and Incomplete Gamma Function, J. Math. and Phys. 38, 77--81 (1959)249
9.2.[10] Exponential Integral [∫][∞]1 e-xt t-n dt for Large Values of n, J. Res. Nat. Bur. Standards 62, 123--125 (1959)255
9.3.[13] Recursive Computation of the Repeated Integrals of the Error Function, Math. Comp. 15, 227--232 (1961)259
9.4.[39] Efficient Computation of the Complex Error Function, SIAM J. Numer. Anal. 7, 187--198 (1970)266
9.5.[47] A Harmonic Mean Inequality for the Gamma Function, SIAM J. Math. Anal. 5, 278--281 (1974)279
9.6.[48] Some Mean Value Inequalities for the Gamma Function, SIAM J. Math. Anal. 5, 282--292 (1974)284
9.7.[49] Computational Methods in Special Functions --- A Survey, in Theory and Applications of Special Functions (R. A. Askey, ed.), 1--98, Math. Res. Center, Univ. Wisconsin Publ. 35 (1975)296
9.8.[61] Anomalous Convergence of a Continued Fraction for Ratios of Kummer Functions, Math. Comp. 31, 994--999 (1977)395
9.9.[68] A Computational Procedure for Incomplete Gamma Functions, ACM Trans. Math. Software 5, 466--481 (1979)402
9.10.[72] (with F. Costabile) Lower Bounds for the Largest Zeros of Orthogonal Polynomials, Boll. Un. Mat. Ital. (5) 17A, 516--522 (1980) (translated from Italian)419
9.11.[155] The Incomplete Gamma Functions Since Tricomi, in Tricomi's Ideas and Contemporary Applied Mathematics, 203--237, Atti Convegni Lincei 147 (1998)428
9.12.[168] Gauss Quadrature Approximations to Hypergeometric and Confluent Hypergeometric Functions, J. Comput. Appl. Math. 139, 173--187 (2002)464
9.13.[169] Computation of Bessel and Airy Functions and of Related Gaussian Quadrature Formulae, BIT 42, 110--118 (2002)480
9.14.[178] Numerical Quadrature Computation of the Macdonald Function for Complex Orders, BIT Numer. Math. 45, 593--603 (2005)490
9.15.[182] (with P. Leopardi) Conjectured Inequalities for Jacobi Polynomials and Their Largest Zeros, Numer. Algorithms 45, 217--230 (2007)502
9.16.[190] On a Conjectured Inequality for the Largest Zero of Jacobi Polynomials, Numer. Algorithms 49, 195--198 (2008)517
9.17.[191] On Conjectured Inequalities for Zeros of Jacobi Polynomials, Numer. Algorithms 50, 93--96 (2009)522
9.18.[192] New Conjectured Inequalities for Zeros of Jacobi Polynomials, Numer. Algorithms 50, 293--296 (2009)527
9.19.[193] How Sharp is Bernstein's Inequality for Jacobi Polynomials?, Electr. Trans. Numer. Anal. 36, 1--8 (2009)532
9.20.[199] The Lambert W-functions and Some of Their Integrals: a Case Study of High-precision Computation, Numer. Algorithms 57, 27--34 (2011)541
9.21.[203] Remark on "New Conjectured Inequalities for Zeros of Jacobi Polynomials by Walter Gautschi, Numer. Algorithms 50: 293--296 (2009)", Numer. Algorithms 57, 511 (2011)550
10.Papers on Interpolation and Approximation553
10.1.[41] Attenuation Factors in Practical Fourier Analysis, Numer. Math. 18, 373--400 (1972)554
10.2.[86] On Pade Approximants Associated with Hamburger Series, Calcolo 20, 111--127 (1983)583
10.3.[87] On the Convergence Behavior of Continued Fractions with Real Elements, Math. Comp. 40, 337--342 (1983)601
10.4.[89] Discrete Approximations to Spherically Symmetric Distributions, Numer. Math. 44, 53--60 (1984)608
10.5.[100] (with G. V. Milovanovic) Spline Approximations to Spherically Symmetric Distributions, Numer. Math. 49, 111--121 (1986)617
10.6.[102] (with M. Frontini and G. V. Milovanovic) Moment-preserving Spline Approximation on Finite Intervals, Numer. Math. 50, 503--518 (1987)629
10.7.[132] On Mean Convergence of Extended Lagrange Interpolation, J. Comput. Appl. Math. 43, 19--35 (1992)646
10.8.[147] (with S. Li) On Quadrature Convergence of Extended Lagrange Interpolation, Math. Comp. 65, 1249--1256 (1996)664
10.9.[165] Remark: "Barycentric Formulae for Cardinal (SINC-) Interpolants" by Jean-Paul Berrut, Numer. Math. 87, 791--792 (2001)673
10.10.[202] Experimental Mathematics Involving Orthogonal Polynomials, in Approximation and Computation --- In Honor of Gradimir V. Milovanovic (W. Gautschi, G. Mastroianni, and Th. M. Rassias, eds.), 117--134, Springer Optim. Appl. 42 (2011)676
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Description 1 online resource
Series Contemporary mathematicians
Contemporary mathematicians.
Contents Preface -- Biography of Walter Gautschi -- A brief summary of my scientific work and highlights of my career -- Publications -- Numerical conditioning -- Special functions -- Interpolation and approximation -- Numerical conditioning -- Special functions -- Interpolation and approximation
Summary Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He is world renowned for his pioneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area. This three-volume set, Walter Gautschi: Selected Works with Commentaries, is a compilation of Gautschis most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemorating Walters prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science. Selected Works with Commentaries, Vol. 1 Numerical Conditioning Special Functions Interpolation and Approximation Selected Works with Commentaries, Vol. 2 Orthogonal Polynomials on the Real Line Orthogonal Polynomials on the Semicircle Chebyshev Quadrature Kronrod and Other Quadratures Gauss-type Quadrature Selected Works with Commentaries, Vol. 3 Linear Difference Equations Ordinary Differential Equations Software History and Biography Miscellanea Works of Werner Gautschi
Analysis Numerical Analysis
Mathematics of Computing
Approximations and Expansions
History of Mathematical Sciences
Ordinary Differential Equations
Mathematics
Bibliography Includes bibliographical references
Notes Print version record
Subject Gautschi, Walter, 1927-
Numerical analysis.
Mathematical Computing.
Form Electronic book
Author Brezinski, Claude, 1941- editor
Sameh, Ahmed, editor
Gautschi, Walter, 1927- Works. Selections
ISBN 146147034X (electronic bk.)
9781461470342 (electronic bk.)