Approximate Solutions

Klaus Deimling
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Klaus Deimling: Gesamthochschule Paderborn

Chapter Chapter 7 in Nonlinear Functional Analysis, 1985, pp 256-277 from Springer

Abstract: Abstract To solve an infinite-dimensional equation Fx = y it is no doubt the most natural elementary approach to replace Fx = y by appropriate finite-dimensional problems F n x = y n and to solve F n x = y n by x n such that (x n ) has at least a subsequence tending to a solution x of Fx = y, if possible. Remember that we used this idea, for example, in the definition of the Leray-Schauder degree and in the proofs of surjectivity results for monotone operators. The abstract formulation of some numerical methods suggests that we perform this approximation more systematically than in the cases just mentioned, by introduction of definite approximation schemes.

Date: 1985
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DOI: 10.1007/978-3-662-00547-7_7

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