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Methods for Solving Incorrectly Posed Problems (Paperback, Softcover reprint of the original 1st ed. 1984) Loot Price: R1,592
Discovery Miles 15 920
Methods for Solving Incorrectly Posed Problems (Paperback, Softcover reprint of the original 1st ed. 1984): A.B. Aries

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

A.B. Aries; Edited by Z. Nashed; V.A Morozov

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Loot Price R1,592 Discovery Miles 15 920 | Repayment Terms: R149 pm x 12*

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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
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LSN: 0-387-96059-7
Barcode: 9780387960593

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