الرياضيات التطبيقية Books in Approximation theory

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    السلام عليكم
    From Wikipedia, the free encyclopedia


    In , approximation theory is concerned with how can best be with simpler , and with the introduced thereby. Note that what is meant by best and simpler will depend on the application.
    A closely related topic is the approximation of functions by , that is, approximations based upon summation of a series of terms based upon .
    One problem of particular interest is that of approximating a function in a mathematical library, using operations that can be performed on the computer or calculator (e.g. addition and multiplication), such that the result is as close to the actual function as possible. This is typically done with or (ratio of polynomials) approximations.
    The objective is to make the approximation as close as possible to the actual function, typically with an accuracy close to that of the underlying computer's arithmetic. This is accomplished by using a polynomial of high degree, and/or narrowing the domain over which the polynomial has to approximate the function. Narrowing the domain can often be done though the use of various addition or scaling formulas for the function being approximated. Modern mathematical libraries often reduce the domain into many tiny segments and use a low-degree polynomial for each segment.


    For more information see





    From CRC Concise Encyclopedia of Mathematics, Second Edition, by Weisstein


    Approximation Theory The mathematical study of how given quantities can be approximated by other (usually simpler) ones under appropriate conditions. Approximation theory also studies the size and properties of the ERROR introduced by approximation. Approximations are often obtained by POWER SERIES expansions in which the higher order terms are dropped.



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    Approximation Theory. Tampa: Proceedings of a Seminar held in Tampa, Florida, 1985 - 1986 (Lecture Notes in Mathematics)
    By Edward B. Saff




    • Publisher: Springer
    • Number Of Pages: 228
    • Publication Date: 1987-11-18
    • ISBN-10 / ASIN: 3540185003
    • ISBN-13 / EAN: 9783540185000
    • Binding: Paperback



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    Methods of Approximation Theory in Complex Analysis and Mathematical Physics: The Euler International Mathematical Institute, Leningrad, May 13-24, 1991 (Lecture Notes in Mathematics)
    By A.A. Gonchar, Edward B. Saff




    • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
    • Number Of Pages: 222
    • Publication Date: 1993-08
    • ISBN-10 / ASIN: 3540569316
    • ISBN-13 / EAN: 9783540569312
    • Binding: Paperback






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    An Introduction to the Approximation of Functions (Blaisdell Book in Numerical Analysis and Computer Science)
    By Theodore J. Rivlin



    • Publisher: Blaisdell Pub. Co
    • Number Of Pages: 150
    • Publication Date: 1969
    • ISBN-10 / ASIN: B0006BYK04
    • ISBN-13 / EAN:
    • Binding: Hardcover











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    Approximation Theory: Proceedings of an International Conference held at Bonn, Germany, June 8-11, 1976 (Lecture Notes in Mathematics)
    By R. Schaback, K. Scherer




    • Publisher: Springer
    • Number Of Pages: 466
    • Publication Date: 1977-01-21
    • ISBN-10 / ASIN: 3540080015
    • ISBN-13 / EAN: 9783540080015
    • Binding: Paperback











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    The application of continued fractions and their generalizations to problems in approximation theory (Library of applied analysis and computational mathematics)
    By A. N Khovanskii




    • Publisher: P. Noordhoff
    • Number Of Pages: 212
    • Publication Date: 1963
    • ISBN-10 / ASIN: B0006BLMYQ
    • ISBN-13 / EAN:
    • Binding: Unknown Binding






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  7. ابو رشاد

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    Polynominal Approximation of Differential Equations (Lecture Notes in Physics)
    By Daniele Funaro



    • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
    • Number Of Pages: 315
    • Publication Date: 1992-04
    • ISBN-10 / ASIN: 3540552308
    • ISBN-13 / EAN: 9783540552307
    • Binding: Paperback



    Essentials of Pade Approximants
    By George A. Baker



    • Publisher: Academic Press Inc
    • Number Of Pages: 306
    • Publication Date: 1975-03-21
    • ISBN-10 / ASIN: 012074855X
    • ISBN-13 / EAN: 9780120748556
    • Binding: Hardcover















    Approximation Theory IX: Volume I: Theoretical Aspects (Vol 1)
    By Charles Chui, Larry L. Schumaker




    • Publisher: Vanderbilt University Press
    • Number Of Pages: 576
    • Publication Date: 1999-01-31
    • ISBN-10 / ASIN: 0826513255
    • ISBN-13 / EAN: 9780826513250
    • Binding: Hardcover





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    Approximation Theory IX: Volume II: Computational Aspects (Vol 2)
    By Charles Chui, Larry L. Schumaker



    • Publisher: Vanderbilt University Press
    • Number Of Pages: 472
    • Publication Date: 1999-01-31
    • ISBN-10 / ASIN: 0826513263
    • ISBN-13 / EAN: 9780826513267
    • Binding: Hardcove



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    Introduction to Approximation Theory (AMS/Chelsea Publication)
    By Elliott W. Cheney



    • Publisher: Amer Mathematical Society
    • Number Of Pages: 259
    • Publication Date: 2000-03-01
    • ISBN-10 / ASIN: 0821813749
    • ISBN-13 / EAN: 9780821813744
    • Binding: Hardcover




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    Pade Approximants, Part 1 (Section, Mathematics of physics)
    By George A. Baker, P.R.Graves- Morris



    • Publisher: Longman Higher Education
    • Number Of Pages: 345
    • Publication Date: 1981-12
    • ISBN-10 / ASIN: 0201135124
    • ISBN-13 / EAN: 9780201135121
    • Binding: Paperback



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    Pade Approximants, Part 2
    By George A. Baker, P.R.Graves- Morris



    • Publisher: Longman Higher Education
    • Number Of Pages: 233
    • Publication Date: 1981-12
    • ISBN-10 / ASIN: 0201135132
    • ISBN-13 / EAN: 9780201135138
    • Binding: Paperback




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    Pade approximants method and its applications to mechanics
    by Editor: Cabannes H.


    • Publisher:
    • Number Of Pages: 267
    • Publication Date: 1976
    • ISBN-10 / ASIN: 354007614X
    • ISBN-13 / EAN: 9783540076148
    • Binding: Unknown Binding



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    Pade Approximants and Their Applications
    By P.R.Graves- Morris



    • Publisher: Academic Press Inc.,U.S.
    • Number Of Pages: 354
    • Publication Date: 1973-03
    • ISBN-10 / ASIN: 0122959507
    • ISBN-13 / EAN: 9780122959509
    • Binding: Hardcover




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    Continued Fractions and Pade Approximants
    By C. Brezinski



    • Publisher: North-Holland
    • Number Of Pages: 382
    • Publication Date: 1991-03
    • ISBN-10 / ASIN: 0444881697
    • ISBN-13 / EAN: 9780444881694
    • Binding: Hardcover




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    History of Continued Fractions and Pade Approximants (Springer Series in Computational Mathematics)
    By Claude Brezinski



    • Publisher: Springer
    • Number Of Pages: 551
    • Publication Date: 1991-01
    • ISBN-10 / ASIN: 0387152865
    • ISBN-13 / EAN: 9780387152868
    • Binding: Hardcover








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  14. ابن الخطاب

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    Trends and Applications in Constructive Approximation (International Series of Numerical Mathematics)
    By Detlef H. Mache, József Szabados, Marcel G. de Bruin



    • Publisher: Birkhäuser Basel
    • Number Of Pages: 281
    • Publication Date: 2005-08-30
    • ISBN-10 / ASIN: 3764371242
    • ISBN-13 / EAN: 9783764371241
    • Binding: Hardcover




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    Analysis II: Convex Analysis and Approximation Theory (Encyclopaedia of Mathematical Sciences)
    By Vladimir M. Tikhomirov, R.V. Gamkrelidze, David Newton



    • Publisher: Springer
    • Number Of Pages: 255
    • Publication Date: 1990-07-02
    • ISBN-10 / ASIN: 3540181792
    • ISBN-13 / EAN: 9783540181798
    • Binding: Hardcover


    Product Description:
    Intended for a wide range of readers, this book covers the main ideas of convex analysis and approximation theory. The author discusses the sources of these two trends in mathematical analysis, develops the main concepts and results, and mentions some beautiful theorems. The relationship of convex analysis to optimization problems, to the calculus of variations, to optimal control and to geometry is considered, and the evolution of the ideas underlying approximation theory, from its origins to the present day, is discussed. The book is addressed both to students who want to acquaint themselves with these trends and to lecturers in mathematical analysis, optimization and numerical methods, as well as to researchers in these fields who would like to tackle the topic as a whole and seek inspiration for its further development.​





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