Methods for Solving Incorrectly Posed Problems (Paperback, Softcover reprint of the original 1st ed. 1984)

Some problems of mathematical physics and analysis can be formulated as the problem of solving the equation f EURO 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 EURO 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.

General

Imprint:	Springer-Verlag New York
Country of origin:	United States
Release date:	November 1984
First published:	1984
Translators:	A.B. Aries
Editors:	Z. Nashed
Authors:	V.A Morozov
Dimensions:	235 x 155 x 14mm (L x W x T)
Format:	Paperback
Pages:	257
Edition:	Softcover reprint of the original 1st ed. 1984
ISBN-13:	978-0-387-96059-3
Categories:	Books > Science & Mathematics > Mathematics > Numerical analysis
LSN:	0-387-96059-7
Barcode:	9780387960593

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