A convergence result for discrete steepest descent in weighted Sobolev spaces. (English) Zbl 0941.65051

Summary: A convergence result is given for discrete descent based on Sobolev gradients arising from differential equations which may be expressed as quadratic forms. The argument is an extension of the result of D. G. Luenberger on Euclidean descent [Introduction to linear and nonlinear programming (1973; Zbl 0571.90051)] and complements the work of J. W. Neuberger on Sobolev descent [Lect. Notes Math. 564, 341-349 (1976; Zbl 0341.35016)].


65J10 Numerical solutions to equations with linear operators
47A50 Equations and inequalities involving linear operators, with vector unknowns
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
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