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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Methods for Solving Incorrectly Posed Problems

Methods for Solving Incorrectly Posed Problems

Nashed, Z.
Morozov, V. a.
Aries, A. B.

Paperback

General Mathematics

ISBN10: 0387960597
ISBN13: 9780387960593
Publisher: Springer
Published: Nov 20 1984
Pages: 257
Weight: 0.87
Height: 0.59 Width: 6.14 Depth: 9.21
Language: English
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.

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