approximation theory and methods

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Approximation Theory And Methods

Author : M. J. D. Powell
ISBN : 0521295149
Genre : Mathematics
File Size : 81. 72 MB
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Most functions that occur in mathematics cannot be used directly in computer calculations. Instead they are approximated by manageable functions such as polynomials and piecewise polynomials. The general theory of the subject and its application to polynomial approximation are classical, but piecewise polynomials have become far more useful during the last twenty years. Thus many important theoretical properties have been found recently and many new techniques for the automatic calculation of approximations to prescribed accuracy have been developed. This book gives a thorough and coherent introduction to the theory that is the basis of current approximation methods. Professor Powell describes and analyses the main techniques of calculation supplying sufficient motivation throughout the book to make it accessible to scientists and engineers who require approximation methods for practical needs. Because the book is based on a course of lectures to third-year undergraduates in mathematics at Cambridge University, sufficient attention is given to theory to make it highly suitable as a mathematical textbook at undergraduate or postgraduate level.

Approximation Theory And Methods

Author : M. J. D. Powell
ISBN : 0521224721
Genre : Mathematics
File Size : 45. 99 MB
Format : PDF, ePub
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Most functions that occur in mathematics cannot be used directly in computer calculations. Instead they are approximated by manageable functions such as polynomials and piecewise polynomials. The general theory of the subject and its application to polynomial approximation are classical, but piecewise polynomials have become far more useful during the last twenty years. Thus many important theoretical properties have been found recently and many new techniques for the automatic calculation of approximations to prescribed accuracy have been developed. This book gives a thorough and coherent introduction to the theory that is the basis of current approximation methods. Professor Powell describes and analyses the main techniques of calculation supplying sufficient motivation throughout the book to make it accessible to scientists and engineers who require approximation methods for practical needs. Because the book is based on a course of lectures to third-year undergraduates in mathematics at Cambridge University, sufficient attention is given to theory to make it highly suitable as a mathematical textbook at undergraduate or postgraduate level.

Approximation Theory And Numerical Methods

Author : G. A. Watson
ISBN : UOM:39015015733853
Genre : Mathematics
File Size : 44. 98 MB
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An Introduction To The Approximation Of Functions

Author : Theodore J. Rivlin
ISBN : 0486640698
Genre : Mathematics
File Size : 36. 40 MB
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Mathematics of Computing -- Numerical Analysis.

Approximation Theory And Approximation Practice

Author : Lloyd N. Trefethen
ISBN : 161197240X
Genre : Mathematics
File Size : 26. 69 MB
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An original and modern treatment of approximation theory for students in applied mathematics. Includes exercises, illustrations and Matlab code.

Methods Of Approximation Theory

Author : Alexander I. Stepanets
ISBN : 9783110195286
Genre : Mathematics
File Size : 39. 3 MB
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Interpolation And Approximation

Author : Philip J. Davis
ISBN : 9780486624952
Genre : Mathematics
File Size : 67. 55 MB
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Intermediate-level survey covers remainder theory, convergence theorems, and uniform and best approximation. Other topics include least square approximation, Hilbert space, orthogonal polynomials, theory of closure and completeness, and more. 1963 edition.

Interpolation And Approximation By Polynomials

Author : George M. Phillips
ISBN : 9780387216829
Genre : Mathematics
File Size : 21. 58 MB
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In addition to coverage of univariate interpolation and approximation, the text includes material on multivariate interpolation and multivariate numerical integration, a generalization of the Bernstein polynomials that has not previously appeared in book form, and a greater coverage of Peano kernel theory than is found in most textbooks. There are many worked examples and each section ends with a number of carefully selected problems that extend the student's understanding of the text. The author is well known for his clarity of writing and his many contributions as a researcher in approximation theory.

Model Reduction And Approximation

Author : Peter Benner
ISBN : 9781611974829
Genre : Science
File Size : 69. 60 MB
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Many physical, chemical, biomedical, and technical processes can be described by partial differential equations or dynamical systems. In spite of increasing computational capacities, many problems are of such high complexity that they are solvable only with severe simplifications, and the design of efficient numerical schemes remains a central research challenge. This book presents a tutorial introduction to recent developments in mathematical methods for model reduction and approximation of complex systems. Model Reduction and Approximation: Theory and Algorithms contains three parts that cover (I) sampling-based methods, such as the reduced basis method and proper orthogonal decomposition, (II) approximation of high-dimensional problems by low-rank tensor techniques, and (III) system-theoretic methods, such as balanced truncation, interpolatory methods, and the Loewner framework. It is tutorial in nature, giving an accessible introduction to state-of-the-art model reduction and approximation methods. It also covers a wide range of methods drawn from typically distinct communities (sampling based, tensor based, system-theoretic).?? This book is intended for researchers interested in model reduction and approximation, particularly graduate students and young researchers.

Introduction To Approximation Theory

Author : Elliott Ward Cheney
ISBN : 0821813749
Genre : Mathematics
File Size : 62. 57 MB
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This volume contains historical background and discussion of results for each chapter, References, and an Index.

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