Download or read book On the Stability of the Discrepancy Method for Solving First Kind Operator Equations with Perturbed Operators written by Nguyen Van Kinh and published by . This book was released on 1989 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Linear Operator Equations Approximation And Regularization written by M Thamban Nair and published by World Scientific. This book was released on 2009-05-05 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in science and engineering have their mathematical formulation as an operator equation Tx=y, where T is a linear or nonlinear operator between certain function spaces. In practice, such equations are solved approximately using numerical methods, as their exact solution may not often be possible or may not be worth looking for due to physical constraints. In such situations, it is desirable to know how the so-called approximate solution approximates the exact solution, and what the error involved in such procedures would be.This book is concerned with the investigation of the above theoretical issues related to approximately solving linear operator equations. The main tools used for this purpose are basic results from functional analysis and some rudimentary ideas from numerical analysis. To make this book more accessible to readers, no in-depth knowledge on these disciplines is assumed for reading this book.
Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 1770 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Solution Methods for Operator Equations of the First Kind written by Petrus Maria Bakker and published by . This book was released on 1982 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Regularization for Applied Inverse and Ill Posed Problems written by Bernd Hofmann and published by Springer. This book was released on 1986-06 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Non iterative Methods for Solving Operator Equations of the First Kind written by John W. Hilgers and published by . This book was released on 1973 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper compares the reproducing kernel Hilbert space method for solving integral equations of the first kind with Tihonov regularization. The methods are theoretically identical and differ in practice only in the way discretization is introduced. Numerical examples are given. (Author).
Download or read book The Classical Stefan Problem written by S.C. Gupta and published by Elsevier. This book was released on 2017-07-27 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Classical Stefan Problem: Basic Concepts, Modelling and Analysis with Quasi-Analytical Solutions and Methods, New Edition, provides the fundamental theory, concepts, modeling, and analysis of the physical, mathematical, thermodynamical, and metallurgical properties of classical Stefan and Stefan-like problems as applied to heat transfer problems with phase-changes, such as from liquid to solid. This self-contained work reports and derives the results from tensor analysis, differential geometry, non-equilibrium thermodynamics, physics, and functional analysis, and is thoroughly enriched with many appropriate references for in-depth background reading on theorems. Each chapter in this fully revised and updated edition begins with basic concepts and objectives, also including direction on how the subject matter was developed. It contains more than 400 pages of new material on quasi-analytical solutions and methods of classical Stefan and Stefan-like problems.The book aims to bridge the gap between the theoretical and solution aspects of the afore-mentioned problems. Provides both the phenomenology and mathematics of Stefan problems Bridges physics and mathematics in a concrete and readable manner Presents well-organized chapters that start with proper definitions followed by explanations and references for further reading Includes both numerical and quasi-analytical solutions and methods of classical Stefan and Stefan-like problems
Download or read book The Princeton Companion to Applied Mathematics written by Nicholas J. Higham and published by Princeton University Press. This book was released on 2015-09-15 with total page 1031 pages. Available in PDF, EPUB and Kindle. Book excerpt: The must-have compendium on applied mathematics This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics. Features nearly 200 entries organized thematically and written by an international team of distinguished contributors Presents the major ideas and branches of applied mathematics in a clear and accessible way Explains important mathematical concepts, methods, equations, and applications Introduces the language of applied mathematics and the goals of applied mathematical research Gives a wide range of examples of mathematical modeling Covers continuum mechanics, dynamical systems, numerical analysis, discrete and combinatorial mathematics, mathematical physics, and much more Explores the connections between applied mathematics and other disciplines Includes suggestions for further reading, cross-references, and a comprehensive index
Download or read book Methods for Solving Operator Equations written by Vitalij P. Tanana and published by VSP. This book was released on 1997 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.
Download or read book U S S R Computational Mathematics and Mathematical Physics written by and published by . This book was released on 1970 with total page 944 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains papers translated from: Zhurnal vychislitelʹnoĭ matematiki i matematicheskoĭ fiziki.
Download or read book Error Estimation and Iterative Improvement for the Numerical Solution of Operator Equations written by Bengt Lindberg and published by . This book was released on 1976 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Method for estimation of the global discretization error of solutions of operator equations is presented. Further an algorithm for iterative improvement of the approximate solution of such problems is given. The theoretical foudation for the algorithms are given as a number of theorems. Several classes of operator equations are examined and numerical results for both the error estimation algorithm and the algorithm for iterative improvement are given for some classes of ordinary and partial differential equations and integral equations. (Author).
Download or read book Inverse Problems written by Alexander G. Ramm and published by Springer Science & Business Media. This book was released on 2005-12-19 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse Problems is a monograph which contains a self-contained presentation of the theory of several major inverse problems and the closely related results from the theory of ill-posed problems. The book is aimed at a large audience which include graduate students and researchers in mathematical, physical, and engineering sciences and in the area of numerical analysis.
Download or read book Methods for Solving Incorrectly Posed Problems written by V.A. Morozov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some problems of mathematical physics and analysis can be formulated as the problem of solving the equation f € F, (1) Au = f, where A: DA C U + F is an operator with a non-empty domain of definition D , in a metric space U, with range in a metric space F. The metrics A on U and F will be denoted by P and P ' respectively. Relative u F to the twin spaces U and F, J. Hadamard P-06] gave the following defini tion of correctness: the problem (1) is said to be well-posed (correct, properly posed) if the following conditions are satisfied: (1) The range of the value Q of the operator A coincides with A F ("sol vabi li ty" condition); (2) The equality AU = AU for any u ,u € DA implies the I 2 l 2 equality u = u ("uniqueness" condition); l 2 (3) The inverse operator A-I is continuous on F ("stability" condition). Any reasonable mathematical formulation of a physical problem requires that conditions (1)-(3) be satisfied. That is why Hadamard postulated that any "ill-posed" (improperly posed) problem, that is to say, one which does not satisfy conditions (1)-(3), is non-physical. Hadamard also gave the now classical example of an ill-posed problem, namely, the Cauchy problem for the Laplace equation.
Download or read book Stability of Solutions to Linear Operator Equations of the First and Second Kinds Under Perturbation of the Operator with Rank Change written by Heinz Engl and published by . This book was released on 1980 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Ill posed Problems of Monotone Type written by Yakov Alber and published by Springer Science & Business Media. This book was released on 2006-02-02 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest in regularization methods for ill-posed nonlinear operator equations and variational inequalities of monotone type in Hilbert and Banach spaces has grown rapidly over recent years. Results in the field over the last three decades, previously only available in journal articles, are comprehensively explored with particular attention given to applications of regularization methods as well as to practical methods used in computational analysis.
Download or read book Conservative Finite Difference Methods on General Grids written by Mikhail Shashkov and published by CRC Press. This book was released on 1995-12-05 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new book deals with the construction of finite-difference (FD) algorithms for three main types of equations: elliptic equations, heat equations, and gas dynamic equations in Lagrangian form. These methods can be applied to domains of arbitrary shapes. The construction of FD algorithms for all types of equations is done on the basis of the support-operators method (SOM). This method constructs the FD analogs of main invariant differential operators of first order such as the divergence, the gradient, and the curl. This book is unique because it is the first book not in Russian to present the support-operators ideas. Conservative Finite-Difference Methods on General Grids is completely self-contained, presenting all the background material necessary for understanding. The book provides the tools needed by scientists and engineers to solve a wide range of practical engineering problems. An abundance of tables and graphs support and explain methods. The book details all algorithms needed for implementation. A 3.5" IBM compatible computer diskette with the main algorithms in FORTRAN accompanies text for easy use.
Download or read book Soviet Mathematics written by Soviet Union. Ministerstvo vysshego i srednego spet︠s︡ialʹnogo obrazovanii︠a︡ and published by . This book was released on 1986 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt:
