Nonlinear Numerical Methods And Rational Approximation Ii

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Nonlinear Numerical Methods and Rational Approximation II

Author : A. Cuyt
Publisher : Springer Science & Business Media
ISBN 13 : 9401109702
Total Pages : 443 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Nonlinear Numerical Methods and Rational Approximation II by : A. Cuyt

Download or read book Nonlinear Numerical Methods and Rational Approximation II written by A. Cuyt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: These are the proceedings of the international conference on "Nonlinear numerical methods and Rational approximation II" organised by Annie Cuyt at the University of Antwerp (Belgium), 05-11 September 1993. It was held for the third time in Antwerp at the conference center of UIA, after successful meetings in 1979 and 1987 and an almost yearly tradition since the early 70's. The following figures illustrate the growing number of participants and their geographical dissemination. In 1993 the Belgian scientific committee consisted of A. Bultheel (Leuven), A. Cuyt (Antwerp), J. Meinguet (Louvain-Ia-Neuve) and J.-P. Thiran (Namur). The conference focused on the use of rational functions in different fields of Numer ical Analysis. The invited speakers discussed "Orthogonal polynomials" (D. S. Lu binsky), "Rational interpolation" (M. Gutknecht), "Rational approximation" (E. B. Saff) , "Pade approximation" (A. Gonchar) and "Continued fractions" (W. B. Jones). In contributed talks multivariate and multidimensional problems, applications and implementations of each main topic were considered. To each of the five main topics a separate conference day was devoted and a separate proceedings chapter compiled accordingly. In this way the proceedings reflect the organisation of the talks at the conference. Nonlinear numerical methods and rational approximation may be a nar row field for the outside world, but it provides a vast playground for the chosen ones. It can fascinate specialists from Moscow to South-Africa, from Boulder in Colorado and from sunny Florida to Zurich in Switzerland.

Nonlinear Methods in Numerical Analysis

Author : A. Cuyt
Publisher : Elsevier
ISBN 13 : 0080872476
Total Pages : 289 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Nonlinear Methods in Numerical Analysis by : A. Cuyt

Download or read book Nonlinear Methods in Numerical Analysis written by A. Cuyt and published by Elsevier. This book was released on 1987-03-01 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: While most textbooks on Numerical Analysis discuss linear techniques for the solution of various numerical problems, this book introduces and illustrates nonlinear methods. It presents several nonlinear techniques resulting mainly from the use of Padé approximants and rational interpolants.

Nonlinear Numerical Methods and Rational Approximation

Author : A. Cuyt
Publisher : Springer Science & Business Media
ISBN 13 : 9400929013
Total Pages : 459 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Nonlinear Numerical Methods and Rational Approximation by : A. Cuyt

Download or read book Nonlinear Numerical Methods and Rational Approximation written by A. Cuyt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gu!ik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; use Stein spaces. And in addition to this there are and prediction and electrical engineering can such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Introduction To The Theory Of Weighted Polynomial Approximation

Author : H N Mhaskar
Publisher : World Scientific
ISBN 13 : 9814518050
Total Pages : 398 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Introduction To The Theory Of Weighted Polynomial Approximation by : H N Mhaskar

Download or read book Introduction To The Theory Of Weighted Polynomial Approximation written by H N Mhaskar and published by World Scientific. This book was released on 1997-01-04 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we have attempted to explain a variety of different techniques and ideas which have contributed to this subject in its course of successive refinements during the last 25 years. There are other books and surveys reviewing the ideas from the perspective of either potential theory or orthogonal polynomials. The main thrust of this book is to introduce the subject from an approximation theory point of view. Thus, the main motivation is to study analogues of results from classical trigonometric approximation theory, introducing other ideas as needed. It is not our objective to survey the most recent results, but merely to introduce to the readers the thought processes and ideas as they are developed.This book is intended to be self-contained, although the reader is expected to be familiar with rudimentary real and complex analysis. It will also help to have studied elementary trigonometric approximation theory, and have some exposure to orthogonal polynomials.

Applied Mechanics Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 568 pages
Book Rating : 4.:/5 (26 download)

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Book Synopsis Applied Mechanics Reviews by :

Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1972 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Approximation and Computation: A Festschrift in Honor of Walter Gautschi

Author : R.V.M. Zahar
Publisher : Springer Science & Business Media
ISBN 13 : 1468474154
Total Pages : 627 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Approximation and Computation: A Festschrift in Honor of Walter Gautschi by : R.V.M. Zahar

Download or read book Approximation and Computation: A Festschrift in Honor of Walter Gautschi written by R.V.M. Zahar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: R. V. M. Zahar* The sixty-fifth birthday of Walter Gautschi provided an opportune moment for an international symposium in his honor, to recognize his many contributions to mathematics and computer sciences. Conceived by John Rice and sponsored by Purdue University, the conference took place in West Lafayette from December 2 to 5, 1993, and was organized around the four main themes representing Professor Gautschi's principal research interests: Approximation, Orthogonal Polynomials, Quadrature and Special Functions. Thirty-eight speakers - colleagues, co-authors, research collaborators or doctoral students of Professor Gautschi - were invited to present articles at the conference, their lectures providing an approximately equal representation of the four disciplines. Five invited speakers, Germund Dahlquist, Philip Davis, Luigi Gatteschi, Werner Rheinboldt and Stephan Ruscheweyh, were unable to present their talks because of illness or other commitments, although Professors Dahlquist, Gatteschi and Ruscheweyh subsequently contributed arti cles to these proceedings. Thus, the final program contained thirty-three technical lectures, ten of which were plenary sessions. Approximately eighty scientists attended the conference, and for some ses sions - in particular, Walter's presentation of his entertaining and informative Reflections and Recollections - that number was complemented by many visitors and friends, as well as the family of the honoree. A surprise visit by Paul Erdos provided one of the highlights of the conference week. The ambiance at the sym posium was extremely collegial, due no doubt to the common academic interests and the personal friendships shared by the participants.

The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations

Author : A.J. Jerri
Publisher : Springer Science & Business Media
ISBN 13 : 1475728476
Total Pages : 357 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations by : A.J. Jerri

Download or read book The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations written by A.J. Jerri and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents the first attempt at a unified picture for the pres ence of the Gibbs (or Gibbs-Wilbraham) phenomenon in applications, its analysis and the different methods of filtering it out. The analysis and filtering cover the familiar Gibbs phenomenon in Fourier series and integral representations of functions with jump discontinuities. In ad dition it will include other representations, such as general orthogonal series expansions, general integral transforms, splines approximation, and continuous as well as discrete wavelet approximations. The mate rial in this book is presented in a manner accessible to upperclassmen and graduate students in science and engineering, as well as researchers who may face the Gibbs phenomenon in the varied applications that in volve the Fourier and the other approximations of functions with jump discontinuities. Those with more advanced backgrounds in analysis will find basic material, results, and motivations from which they can begin to develop deeper and more general results. We must emphasize that the aim of this book (the first on the sUbject): to satisfy such a diverse audience, is quite difficult. In particular, our detailed derivations and their illustrations for an introductory book may very well sound repeti tive to the experts in the field who are expecting a research monograph. To answer the concern of the researchers, we can only hope that this book will prove helpful as a basic reference for their research papers.

Pade Approximants

Author : George Allen Baker
Publisher : Cambridge University Press
ISBN 13 : 0521450071
Total Pages : 762 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis Pade Approximants by : George Allen Baker

Download or read book Pade Approximants written by George Allen Baker and published by Cambridge University Press. This book was released on 1996-01-26 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this book was reviewed in 1982 as "the most extensive treatment of Pade approximants actually available." This second edition has been thoroughly updated, with a substantial new chapter on multiseries approximants. Applications to statistical mechanics and critical phenomena are extensively covered, and there are newly extended sections devoted to circuit design, matrix Pade approximation, and computational methods. This succinct and straightforward treatment will appeal to scientists, engineers, and mathematicians alike.

Computational Aspects of Linear Control

Author : Claude Brezinski
Publisher : Springer Science & Business Media
ISBN 13 : 1461302617
Total Pages : 296 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Computational Aspects of Linear Control by : Claude Brezinski

Download or read book Computational Aspects of Linear Control written by Claude Brezinski and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many devices (we say dynamical systems or simply systems) behave like black boxes: they receive an input, this input is transformed following some laws (usually a differential equation) and an output is observed. The problem is to regulate the input in order to control the output, that is for obtaining a desired output. Such a mechanism, where the input is modified according to the output measured, is called feedback. The study and design of such automatic processes is called control theory. As we will see, the term system embraces any device and control theory has a wide variety of applications in the real world. Control theory is an interdisci plinary domain at the junction of differential and difference equations, system theory and statistics. Moreover, the solution of a control problem involves many topics of numerical analysis and leads to many interesting computational problems: linear algebra (QR, SVD, projections, Schur complement, structured matrices, localization of eigenvalues, computation of the rank, Jordan normal form, Sylvester and other equations, systems of linear equations, regulariza tion, etc), root localization for polynomials, inversion of the Laplace transform, computation of the matrix exponential, approximation theory (orthogonal poly nomials, Pad6 approximation, continued fractions and linear fractional transfor mations), optimization, least squares, dynamic programming, etc. So, control theory is also a. good excuse for presenting various (sometimes unrelated) issues of numerical analysis and the procedures for their solution. This book is not a book on control.

Linear Difference Equations with Discrete Transform Methods

Author : A.J. Jerri
Publisher : Springer Science & Business Media
ISBN 13 : 1475756577
Total Pages : 456 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Linear Difference Equations with Discrete Transform Methods by : A.J. Jerri

Download or read book Linear Difference Equations with Discrete Transform Methods written by A.J. Jerri and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the basic elements of difference equations and the tools of difference and sum calculus necessary for studying and solv ing, primarily, ordinary linear difference equations. Examples from various fields are presented clearly in the first chapter, then discussed along with their detailed solutions in Chapters 2-7. The book is in tended mainly as a text for the beginning undergraduate course in difference equations, where the "operational sum calculus" of the di rect use of the discrete Fourier transforms for solving boundary value problems associated with difference equations represents an added new feature compared to other existing books on the subject at this introductory level. This means that in addition to the familiar meth ods of solving difference equations that are covered in Chapter 3, this book emphasizes the use of discrete transforms. It is an attempt to introduce the methods and mechanics of discrete transforms for solv ing ordinary difference equations. The treatment closely parallels what many students have already learned about using the opera tional (integral) calculus of Laplace and Fourier transforms to solve differential equations. As in the continuous case, discrete operational methods may not solve problems that are intractable by other meth ods, but they can facilitate the solution of a large class of discrete initial and boundary value problems. Such operational methods, or what we shall term "operational sum calculus," may be extended eas ily to solve partial difference equations associated with initial and/or boundary value problems.

Elimination Methods in Polynomial Computer Algebra

Author : V. Bykov
Publisher : Springer Science & Business Media
ISBN 13 : 9401153027
Total Pages : 254 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Elimination Methods in Polynomial Computer Algebra by : V. Bykov

Download or read book Elimination Methods in Polynomial Computer Algebra written by V. Bykov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this book is connected with a new direction in mathematics, which has been actively developed over the last few years, namely the field of polynomial computer algebra, which lies at the intersection point of algebra, mathematical analysis and programming. There were several incentives to write the book. First of all, there has lately been a considerable interest in applied nonlinear problems characterized by multiple sta tionary states. Practical needs have then in their turn led to the appearance of new theoretical results in the analysis of systems of nonlinear algebraic equations. And finally, the introduction of various computer packages for analytic manipulations has made it possible to use complicated elimination-theoretical algorithms in prac tical research. The structure of the book is accordingly represented by three main parts: Mathematical results driven to constructive algorithms, computer algebra realizations of these algorithms, and applications. Nonlinear systems of algebraic equations arise in diverse fields of science. In particular, for processes described by systems of differential equations with a poly nomial right hand side one is faced with the problem of determining the number (and location) of the stationary states in certain sets.

Handbook of Multivalued Analysis

Author : Shouchuan Hu
Publisher : Springer Science & Business Media
ISBN 13 : 1461546656
Total Pages : 941 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Handbook of Multivalued Analysis by : Shouchuan Hu

Download or read book Handbook of Multivalued Analysis written by Shouchuan Hu and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 941 pages. Available in PDF, EPUB and Kindle. Book excerpt: In volume I we developed the tools of "Multivalued Analysis. " In this volume we examine the applications. After all, the initial impetus for the development of the theory of set-valued functions came from its applications in areas such as control theory and mathematical economics. In fact, the needs of control theory, in particular the study of systems with a priori feedback, led to the systematic investigation of differential equations with a multi valued vector field (differential inclusions). For this reason, we start this volume with three chapters devoted to set-valued differential equations. However, in contrast to the existing books on the subject (i. e. J. -P. Aubin - A. Cellina: "Differential Inclusions," Springer-Verlag, 1983, and Deimling: "Multivalued Differential Equations," W. De Gruyter, 1992), here we focus on "Evolution Inclusions," which are evolution equations with multi valued terms. Evolution equations were raised to prominence with the development of the linear semigroup theory by Hille and Yosida initially, with subsequent im portant contributions by Kato, Phillips and Lions. This theory allowed a successful unified treatment of some apparently different classes of nonstationary linear par tial differential equations and linear functional equations. The needs of dealing with applied problems and the natural tendency to extend the linear theory to the nonlinear case led to the development of the nonlinear semigroup theory, which became a very effective tool in the analysis of broad classes of nonlinear evolution equations.

Boolean Valued Analysis

Author : A. G. Kusraev
Publisher : Springer Science & Business Media
ISBN 13 : 9780792359210
Total Pages : 352 pages
Book Rating : 4.3/5 (592 download)

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Book Synopsis Boolean Valued Analysis by : A. G. Kusraev

Download or read book Boolean Valued Analysis written by A. G. Kusraev and published by Springer Science & Business Media. This book was released on 1999 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boolean valued analysis is a technique for studying properties of an arbitrary mathematical object by comparing its representations in two different set-theoretic models whose construction utilises principally distinct Boolean algebras. The use of two models for studying a single object is a characteristic of the so-called non-standard methods of analysis. Application of Boolean valued models to problems of analysis rests ultimately on the procedures of ascending and descending, the two natural functors acting between a new Boolean valued universe and the von Neumann universe.

Walter Gautschi, Volume 2

Author : Claude Brezinski
Publisher : Springer Science & Business Media
ISBN 13 : 1461470498
Total Pages : 921 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Walter Gautschi, Volume 2 by : Claude Brezinski

Download or read book Walter Gautschi, Volume 2 written by Claude Brezinski and published by Springer Science & Business Media. This book was released on 2013-10-22 with total page 921 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Gautschi’s most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemorating Walter’s 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

Oscillation Theory of Two-Term Differential Equations

Author : Elias Uri
Publisher : Springer Science & Business Media
ISBN 13 : 9780792344476
Total Pages : 238 pages
Book Rating : 4.3/5 (444 download)

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Book Synopsis Oscillation Theory of Two-Term Differential Equations by : Elias Uri

Download or read book Oscillation Theory of Two-Term Differential Equations written by Elias Uri and published by Springer Science & Business Media. This book was released on 1997-03-31 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Oscillation theory was born with Sturm's work in 1836. It has been flourishing for the past fifty years. Nowadays it is a full, self-contained discipline, turning more towards nonlinear and functional differential equations. Oscillation theory flows along two main streams. The first aims to study prop erties which are common to all linear differential equations. The other restricts its area of interest to certain families of equations and studies in maximal details phenomena which characterize only those equations. Among them we find third and fourth order equations, self adjoint equations, etc. Our work belongs to the second type and considers two term linear equations modeled after y(n) + p(x)y = O. More generally, we investigate LnY + p(x)y = 0, where Ln is a disconjugate operator and p(x) has a fixed sign. These equations enjoy a very rich structure and are the natural generalization of the Sturm-Liouville operator. Results about such equations are distributed over hundreds of research papers, many of them are reinvented again and again and the same phenomenon is frequently discussed from various points of view and different definitions of the authors. Our aim is to introduce an order into this plenty and arrange it in a unified and self contained way. The results are readapted and presented in a unified approach. In many cases completely new proofs are given and in no case is the original proof copied verbatim. Many new results are included.

Logarithms and Antilogarithms

Author : D. Przeworska-Rolewicz
Publisher : Springer Science & Business Media
ISBN 13 : 9401152128
Total Pages : 367 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Logarithms and Antilogarithms by : D. Przeworska-Rolewicz

Download or read book Logarithms and Antilogarithms written by D. Przeworska-Rolewicz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume proposes and explores a new definition of logarithmic mappings as invertible selectors of multifunctions induced by linear operators with domains and ranges in an algebra over a field of characteristic zero. Several important previously published results are presented. Amongst the applications of logarithmic and antilogarithmic mappings are the solution of linear and nonlinear equations in algebras of square matrices. Some results may also provide numerical algorithms for the approximation of solutions. Audience: Research mathematicians and other scientists of other disciplines whose work involves the solution of equations.

Banach Space Complexes

Author : C.-G. Ambrozie
Publisher : Springer Science & Business Media
ISBN 13 : 9401103755
Total Pages : 218 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Banach Space Complexes by : C.-G. Ambrozie

Download or read book Banach Space Complexes written by C.-G. Ambrozie and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this work is to initiate a systematic study of those properties of Banach space complexes that are stable under certain perturbations. A Banach space complex is essentially an object of the form 1 op-l oP +1 ... --+ XP- --+ XP --+ XP --+ ... , where p runs a finite or infiniteinterval ofintegers, XP are Banach spaces, and oP : Xp ..... Xp+1 are continuous linear operators such that OPOp-1 = 0 for all indices p. In particular, every continuous linear operator S : X ..... Y, where X, Yare Banach spaces, may be regarded as a complex: O ..... X ~ Y ..... O. The already existing Fredholm theory for linear operators suggested the possibility to extend its concepts and methods to the study of Banach space complexes. The basic stability properties valid for (semi-) Fredholm operators have their counterparts in the more general context of Banach space complexes. We have in mind especially the stability of the index (i.e., the extended Euler characteristic) under small or compact perturbations, but other related stability results can also be successfully extended. Banach (or Hilbert) space complexes have penetrated the functional analysis from at least two apparently disjoint directions. A first direction is related to the multivariable spectral theory in the sense of J. L.