Books > Science & Mathematics > Mathematics > Numerical analysis
|
Buy Now
Methods for Solving Incorrectly Posed Problems (Paperback, Softcover reprint of the original 1st ed. 1984)
Loot Price: R1,517
Discovery Miles 15 170
|
|
Methods for Solving Incorrectly Posed Problems (Paperback, Softcover reprint of the original 1st ed. 1984)
Expected to ship within 10 - 15 working days
|
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
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!
|
You might also like..
|
Email address subscribed successfully.
A activation email has been sent to you.
Please click the link in that email to activate your subscription.