The Chebyshev Polynomials

Author : J.C. Mason,David C. Handscomb
Publisher : CRC Press
Page : 358 pages
File Size : 46,6 Mb
Release : 2002-09-17
Category : Mathematics
ISBN : 9781420036114

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Chebyshev Polynomials by J.C. Mason,David C. Handscomb Pdf

Chebyshev polynomials crop up in virtually every area of numerical analysis, and they hold particular importance in recent advances in subjects such as orthogonal polynomials, polynomial approximation, numerical integration, and spectral methods. Yet no book dedicated to Chebyshev polynomials has been published since 1990, and even that work focuse

Author : Theodore J. Rivlin
Publisher : Wiley-Interscience
Page : 200 pages
File Size : 54,7 Mb
Release : 1974
Category : Mathematics
ISBN : MINN:319510004728748

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The Chebyshev Polynomials by Theodore J. Rivlin Pdf

Author : Arnold Noah Lowan
Publisher : Unknown
Page : 24 pages
File Size : 45,7 Mb
Release : 1958
Category : Chebyshev polynomials
ISBN : UOM:39015077592965

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On the Use of Chebyshev Polynomials in Numerical Analysis by Arnold Noah Lowan Pdf

This report discusses the use of Chebyshev polynomials in the problem of interpolation and curve fitting and in the very important problem of obtaining "economized expansions" of differential equations, either in the form of polynomials in x or in the form of polynomials in 1/x.

Author : John P. Boyd
Publisher : Courier Corporation
Page : 690 pages
File Size : 40,6 Mb
Release : 2001-12-03
Category : Mathematics
ISBN : 9780486411835

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Chebyshev and Fourier Spectral Methods by John P. Boyd Pdf

Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.

Author : Themistocles M. Rassias,H. M. Srivastava
Publisher : World Scientific
Page : 658 pages
File Size : 44,5 Mb
Release : 1993
Category : Mathematics
ISBN : 9810206143

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Topics in Polynomials of One and Several Variables and Their Applications by Themistocles M. Rassias,H. M. Srivastava Pdf

This volume presents an account of some of the most important work that has been done on various research problems in the theory of polynomials of one and several variables and their applications. It is dedicated to P L Chebyshev, a leading Russian mathematician.

Author : Theodore J. Rivlin
Publisher : Courier Dover Publications
Page : 271 pages
File Size : 41,7 Mb
Release : 2020-08-12
Category : Mathematics
ISBN : 9780486842332

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Chebyshev Polynomials by Theodore J. Rivlin Pdf

This survey of the most important properties of Chebyshev polynomials encompasses several areas of mathematical analysis: • Interpolation theory • Orthogonal polynomials • Approximation theory • Numerical integration • Numerical analysis • Ergodic theory Starting with some definitions and descriptions of elementary properties, the treatment advances to examinations of extremal properties, the expansion of functions in a series of Chebyshev polynomials, and iterative properties. The final chapter explores selected algebraic and number theoretic properties of the Chebyshev polynomials. For advanced undergraduates and graduate students in mathematics Originally published in 1974, the text was updated in 1990; this reprint of the second edition corrects various errors and features new material.

Author : Weidong Guo,Gérard Labrosse,Ranga Narayanan
Publisher : Springer Science & Business Media
Page : 238 pages
File Size : 53,9 Mb
Release : 2013-01-26
Category : Science
ISBN : 9783642340888

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The Application of the Chebyshev-Spectral Method in Transport Phenomena by Weidong Guo,Gérard Labrosse,Ranga Narayanan Pdf

Transport phenomena problems that occur in engineering and physics are often multi-dimensional and multi-phase in character. When taking recourse to numerical methods the spectral method is particularly useful and efficient. The book is meant principally to train students and non-specialists to use the spectral method for solving problems that model fluid flow in closed geometries with heat or mass transfer. To this aim the reader should bring a working knowledge of fluid mechanics and heat transfer and should be readily conversant with simple concepts of linear algebra including spectral decomposition of matrices as well as solvability conditions for inhomogeneous problems. The book is neither meant to supply a ready-to-use program that is all-purpose nor to go through all manners of mathematical proofs. The focus in this tutorial is on the use of the spectral methods for space discretization, because this is where most of the difficulty lies. While time dependent problems are also of great interest, time marching procedures are dealt with by briefly introducing and providing a simple, direct, and efficient method. Many examples are provided in the text as well as numerous exercises for each chapter. Several of the examples are attended by subtle points which the reader will face while working them out. Some of these points are deliberated upon in endnotes to the various chapters, others are touched upon in the book itself.

Author : Charles B. (Charles Burton) Dunham,University of Western Ontario. Department of Computer Science
Publisher : London : Department of Computer Science, University of Western Ontario
Page : 12 pages
File Size : 50,7 Mb
Release : 2003
Category : Electronic
ISBN : 0771424213

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Generalization of Chebyshev Polynomials by Charles B. (Charles Burton) Dunham,University of Western Ontario. Department of Computer Science Pdf

Author : United States. National Bureau of Standards
Publisher : Unknown
Page : 206 pages
File Size : 55,9 Mb
Release : 1952
Category : Chebyshev polynomials
ISBN : UOM:39015026573702

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Tables of Chebyshev Polynomials, Sn(X0 and Cn(X). by United States. National Bureau of Standards Pdf

Author : Björn Engquist
Publisher : Springer
Page : 0 pages
File Size : 53,7 Mb
Release : 2015-11-12
Category : Mathematics
ISBN : 3540705287

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Encyclopedia of Applied and Computational Mathematics by Björn Engquist Pdf

EACM is a comprehensive reference work covering the vast field of applied and computational mathematics. Applied mathematics itself accounts for at least 60 per cent of mathematics, and the emphasis on computation reflects the current and constantly growing importance of computational methods in all areas of applications. EACM emphasizes the strong links of applied mathematics with major areas of science, such as physics, chemistry, biology, and computer science, as well as specific fields like atmospheric ocean science. In addition, the mathematical input to modern engineering and technology form another core component of EACM.

Author : United States. National Bureau of Standards. Computation Laboratory
Publisher : Unknown
Page : 198 pages
File Size : 43,5 Mb
Release : 1952
Category : Chebyshev polynomials
ISBN : UCR:31210000942936

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Tables of Chebyshev Polynomials by United States. National Bureau of Standards. Computation Laboratory Pdf

Author : Charles B. (Charles Burton) Dunham,University of Western Ontario. Department of Computer Science
Publisher : London : Department of Computer Science, University of Western Ontario
Page : 14 pages
File Size : 44,5 Mb
Release : 2003
Category : Electronic
ISBN : 0771424647

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Generalization of Chebyshev Polynomials. II by Charles B. (Charles Burton) Dunham,University of Western Ontario. Department of Computer Science Pdf

Author : Lloyd N. Trefethen
Publisher : SIAM
Page : 375 pages
File Size : 53,5 Mb
Release : 2019-01-01
Category : Mathematics
ISBN : 9781611975949

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Approximation Theory and Approximation Practice, Extended Edition by Lloyd N. Trefethen Pdf

This is a textbook on classical polynomial and rational approximation theory for the twenty-first century. Aimed at advanced undergraduates and graduate students across all of applied mathematics, it uses MATLAB to teach the field’s most important ideas and results. Approximation Theory and Approximation Practice, Extended Edition differs fundamentally from other works on approximation theory in a number of ways: its emphasis is on topics close to numerical algorithms; concepts are illustrated with Chebfun; and each chapter is a PUBLISHable MATLAB M-file, available online. The book centers on theorems and methods for analytic functions, which appear so often in applications, rather than on functions at the edge of discontinuity with their seductive theoretical challenges. Original sources are cited rather than textbooks, and each item in the bibliography is accompanied by an editorial comment. In addition, each chapter has a collection of exercises, which span a wide range from mathematical theory to Chebfun-based numerical experimentation. This textbook is appropriate for advanced undergraduate or graduate students who have an understanding of numerical analysis and complex analysis. It is also appropriate for seasoned mathematicians who use MATLAB.

Author : Adhemar Bultheel,Ronald Cools
Publisher : World Scientific
Page : 240 pages
File Size : 43,5 Mb
Release : 2010
Category : Mathematics
ISBN : 9789812836267

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The Birth of Numerical Analysis by Adhemar Bultheel,Ronald Cools Pdf

The 1947 paper by John von Neumann and Herman Goldstine, OC Numerical Inverting of Matrices of High OrderOCO ( Bulletin of the AMS, Nov. 1947), is considered as the birth certificate of numerical analysis. Since its publication, the evolution of this domain has been enormous. This book is a unique collection of contributions by researchers who have lived through this evolution, testifying about their personal experiences and sketching the evolution of their respective subdomains since the early years. Sample Chapter(s). Chapter 1: Some pioneers of extrapolation methods (323 KB). Contents: Some Pioneers of Extrapolation Methods (C Brezinski); Very Basic Multidimensional Extrapolation Quadrature (J N Lyness); Numerical Methods for Ordinary Differential Equations: Early Days (J C Butcher); Interview with Herbert Bishop Keller (H M Osinga); A Personal Perspective on the History of the Numerical Analysis of Fredholm Integral Equations of the Second Kind (K Atkinson); Memoires on Building on General Purpose Numerical Algorithms Library (B Ford); Recent Trends in High Performance Computing (J J Dongarra et al.); Nonnegativity Constraints in Numerical Analysis (D-H Chen & R J Plemmons); On Nonlinear Optimization Since 1959 (M J D Powell); The History and Development of Numerical Analysis in Scotland: A Personal Perspective (G Alistair Watson); Remembering Philip Rabinowitz (P J Davis & A S Fraenkel); My Early Experiences with Scientific Computation (P J Davis); Applications of Chebyshev Polynomials: From Theoretical Kinematics to Practical Computations (R Piessens). Readership: Mathematicians in numerical analysis and mathematicians who are interested in the history of mathematics.

Author : Charles B. (Charles Burton) Dunham,University of Western Ontario. Department of Computer Science
Publisher : London : Department of Computer Science, University of Western Ontario
Page : 8 pages
File Size : 43,9 Mb
Release : 2000
Category : Electronic
ISBN : 0771422660

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Application of New Classes of "Chebyshev Polynomials" by Charles B. (Charles Burton) Dunham,University of Western Ontario. Department of Computer Science Pdf