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Books in Numerical analysis

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31-40 of 70 results in All results

Dynamical Systems Method for Solving Nonlinear Operator Equations

  • 1st Edition
  • Volume 208
  • September 25, 2006
  • Alexander G. Ramm
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 4 6 5 5 6 - 2
Dynamical Systems Method for Solving Nonlinear Operator Equations is of interest to graduate students in functional analysis, numerical analysis, and ill-posed and inverse problems especially. The book presents a general method for solving operator equations, especially nonlinear and ill-posed. It requires a fairly modest background and is essentially self-contained. All the results are proved in the book, and some of the background material is also included. The results presented are mostly obtained by the author.

Elliptic Boundary Value Problems of Second Order in Piecewise Smooth Domains

  • 1st Edition
  • Volume 69
  • January 12, 2006
  • Michail Borsuk + 1 more
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 4 6 1 7 3 - 1
The book contains a systematic treatment of the qualitative theory of elliptic boundary value problems for linear and quasilinear second order equations in non-smooth domains. The authors concentrate on the following fundamental results: sharp estimates for strong and weak solutions, solvability of the boundary value problems, regularity assertions for solutions near singular points.Key features:* New the Hardy – Friedrichs – Wirtinger type inequalities as well as new integral inequalities related to the Cauchy problem for a differential equation.* Precise exponents of the solution decreasing rate near boundary singular points and best possible conditions for this.* The question about the influence of the coefficients smoothness on the regularity of solutions.* New existence theorems for the Dirichlet problem for linear and quasilinear equations in domains with conical points.* The precise power modulus of continuity at singular boundary point for solutions of the Dirichlet, mixed and the Robin problems.* The behaviour of weak solutions near conical point for the Dirichlet problem for m – Laplacian.* The behaviour of weak solutions near a boundary edge for the Dirichlet and mixed problem for elliptic quasilinear equations with triple degeneration.

Student Solutions Manual to Boundary Value Problems

  • 5th Edition
  • November 16, 2005
  • David L. Powers
  • English
  • Paperback
    9 7 8 - 0 - 1 2 - 0 8 8 5 8 6 - 2
  • eBook
    9 7 8 - 0 - 0 8 - 0 9 1 6 7 3 - 6
This student solutions manual accompanies the text, Boundary Value Problems and Partial Differential Equations, 5e. The SSM is available in print via PDF or electronically, and provides the student with the detailed solutions of the odd-numbered problems contained throughout the book.

Topics in Multivariate Approximation and Interpolation

  • 1st Edition
  • Volume 12
  • November 15, 2005
  • Kurt Jetter + 4 more
  • English
  • Hardback
    9 7 8 - 0 - 4 4 4 - 5 1 8 4 4 - 6
  • eBook
    9 7 8 - 0 - 0 8 - 0 4 6 2 0 4 - 2
This book is a collection of eleven articles, written by leading experts and dealing with special topics in Multivariate Approximation and Interpolation. The material discussed here has far-reaching applications in many areas of Applied Mathematics, such as in Computer Aided Geometric Design, in Mathematical Modelling, in Signal and Image Processing and in Machine Learning, to mention a few. The book aims at giving a comprehensive information leading the reader from the fundamental notions and results of each field to the forefront of research. It is an ideal and up-to-date introduction for graduate students specializing in these topics, and for researchers in universities and in industry.

Ten Mathematical Essays on Approximation in Analysis and Topology

  • 1st Edition
  • April 26, 2005
  • Juan Ferrera + 2 more
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 4 5 9 1 9 - 6
This book collects 10 mathematical essays on approximation in Analysis and Topology by some of the most influent mathematicians of the last third of the 20th Century. Besides the papers contain the very ultimate results in each of their respective fields, many of them also include a series of historical remarks about the state of mathematics at the time they found their most celebrated results, as well as some of their personal circumstances originating them, which makes particularly attractive the book for all scientist interested in these fields, from beginners to experts. These gem pieces of mathematical intra-history should delight to many forthcoming generations of mathematicians, who will enjoy some of the most fruitful mathematics of the last third of 20th century presented by their own authors.This book covers a wide range of new mathematical results. Among them, the most advanced characterisations of very weak versions of the classical maximum principle, the very last results on global bifurcation theory, algebraic multiplicities, general dependencies of solutions of boundary value problems with respect to variations of the underlying domains, the deepest available results in rapid monotone schemes applied to the resolution of non-linear boundary value problems, the intra-history of the the genesis of the first general global continuation results in the context of periodic solutions of nonlinear periodic systems, as well as the genesis of the coincidence degree, some novel applications of the topological degree for ascertaining the stability of the periodic solutions of some classical families of periodic second order equations, the resolution of a number of conjectures related to some very celebrated approximation problems in topology and inverse problems, as well as a number of applications to engineering, an extremely sharp discussion of the problem of approximating topological spaces by polyhedra using various techniques based on inverse systems, as well as homotopy expansions, and the Bishop-Phelps theorem.Key features:- It contains a number of seminal contributions by some of the most world leading mathematicians of the second half of the 20th Century. - The papers cover a complete range of topics, from the intra-history of the involved mathematics to the very last developments in Differential Equations, Inverse Problems, Analysis, Nonlinear Analysis and Topology. - All contributed papers are self-contained works containing rather complete list of references on each of the subjects covered. - The book contains some of the very last findings concerning the maximum principle, the theory of monotone schemes in nonlinear problems, the theory of algebraic multiplicities, global bifurcation theory, dynamics of periodic equations and systems, inverse problems and approximation in topology. - The papers are extremely well written and directed to a wide audience, from beginners to experts. An excellent occasion to become engaged with some of the most fruitful mathematics developed during the last decades.

Krylov Solvers for Linear Algebraic Systems

  • 1st Edition
  • Volume 11
  • September 8, 2004
  • Charles George Broyden + 1 more
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 4 7 8 8 7 - 6
The first four chapters of this book give a comprehensive and unified theory of the Krylov methods. Many of these are shown to be particular examples ofthe block conjugate-gradient algorithm and it is this observation thatpermits the unification of the theory. The two major sub-classes of thosemethods, the Lanczos and the Hestenes-Stiefel, are developed in parallel asnatural generalisations of the Orthodir (GCR) and Orthomin algorithms. Theseare themselves based on Arnoldi's algorithm and a generalised Gram-Schmidtalgorithm and their properties, in particular their stability properties,are determined by the two matrices that define the block conjugate-gradientalgorithm. These are the matrix of coefficients and the preconditioningmatrix.In Chapter 5 the"transpose-free" algorithms based on the conjugate-gradient squared algorithm are presented while Chapter 6 examines the various ways in which the QMR technique has been exploited. Look-ahead methods and general block methods are dealt with in Chapters 7 and 8 while Chapter 9 is devoted to error analysis of two basic algorithms.In Chapter 10 the results of numerical testing of the more important algorithms in their basic forms (i.e. without look-ahead or preconditioning) are presented and these are related to the structure of the algorithms and the general theory. Graphs illustrating the performances of various algorithm/problem combinations are given via a CD-ROM.Chapter 11, by far the longest, gives a survey of preconditioning techniques. These range from the old idea of polynomial preconditioning via SOR and ILU preconditioning to methods like SpAI, AInv and the multigrid methods that were developed specifically for use with parallel computers. Chapter 12 is devoted to dual algorithms like Orthores and the reverse algorithms of Hegedus. Finally certain ancillary matters like reduction to Hessenberg form, Chebychev polynomials and the companion matrix are described in a series of appendices.

Handbook of Differential Equations: Evolutionary Equations

  • 1st Edition
  • Volume 1
  • August 24, 2004
  • C.M. Dafermos + 1 more
  • English
  • Hardback
    9 7 8 - 0 - 4 4 4 - 5 1 1 3 1 - 7
  • eBook
    9 7 8 - 0 - 0 8 - 0 5 2 1 8 2 - 4
This book contains several introductory texts concerning the main directions in the theory of evolutionary partial differential equations. The main objective is to present clear, rigorous,and in depth surveys on the most important aspects of the present theory. The table of contents includes: W.Arendt: Semigroups and evolution equations: Calculus, regularity and kernel estimatesA.Bressan: The front tracking method for systems of conservation lawsE.DiBenedetto, J.M.Urbano,V.Vespri: Current issues on singular and degenerate evolution equations;L.Hsiao, S.Jiang: Nonlinear hyperbolic-parabolic coupled systemsA.Lunardi: Nonlinear parabolic equations and systemsD.Serre:L1-stability of nonlinear waves in scalar conservation laws B.Perthame:Kinetic formulations of parabolic and hyperbolic PDE’s: from theory to numerics

Reliable Methods for Computer Simulation

  • 1st Edition
  • Volume 33
  • July 25, 2004
  • Pekka Neittaanmäki + 1 more
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 5 4 0 5 0 - 4
Recent decades have seen a very rapid success in developing numerical methods based on explicit control over approximation errors. It may be said that nowadays a new direction is forming in numerical analysis, the main goal of which is to develop methods ofreliable computations. In general, a reliable numerical method must solve two basic problems: (a) generate a sequence of approximations that converges to a solution and (b) verify the accuracy of these approximations. A computer code for such a method must consist of two respective blocks: solver and checker.In this book, we are chiefly concerned with the problem (b) and try to present the main approaches developed for a posteriori error estimation in various problems.The authors try to retain a rigorous mathematical style, however, proofs are constructive whenever possible and additional mathematical knowledge is presented when necessary. The book contains a number of new mathematical results and lists a posteriori error estimation methods that have been developed in the very recent time.

Computational Models for the Human Body: Special Volume

  • 1st Edition
  • Volume 12
  • July 16, 2004
  • Nicholas Philippe Ayache
  • English
  • Hardback
    9 7 8 - 0 - 4 4 4 - 5 1 5 6 6 - 7
Provides a better understanding of the physiological and mechanical behaviour of the human body and the design of tools for their realistic numerical simulations, including concrete examples of such computational models. This book covers a large range of methods and an illustrative set of applications.