Minimax approximate solutions of linear boundary value problems
Authors:
Darrell Schmidt and Kenneth L. Wiggins
Journal:
Math. Comp. 33 (1979), 139148
MSC:
Primary 65L10
MathSciNet review:
514815
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Abstract: Define the operator by where and consider the two point boundary value problem , , , where , and . Let denote the set of polynomials of degree at most k and define the approximating set . Then for each there exists satisfying , where denotes the uniform norm on . If the homogeneous BVP , has no nontrivial solutions, then the nonhomogeneous BVP has a unique solution y and for . If X denotes a closed subset of and then for each there exists such that implies that , where denotes the density of X in . Several numerical examples are given.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0025571819790514815X
PII:
S 00255718(1979)0514815X
Keywords:
Minimax approximate solution,
uniform approximation,
boundary value problem
Article copyright:
© Copyright 1979
American Mathematical Society
