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Functional Analysis Techniques In Numerical Analysis, Kenneth D. Schoenfeld
Functional Analysis Techniques In Numerical Analysis, Kenneth D. Schoenfeld
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
In this paper we will consider the problem of selecting the best, or optimal, numerical method of solution to a given mathematical problem. The admissible numerical methods will be a clearly defined set for each problem. Obviously, in order to find the best method in this set, we must have a clear mathematical formulation of just what "best" means; this will be the intent of Theorem 0.1. Intuitively, the best method will be understood to be the one which minimizes the maximum possible error where this error will be measured in terms of the norm of a given Hilbert space. …