A convergence result for discrete steepest descent in weighted Sobolev spaces (Q1809789)

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 \textit{D. G. Luenberger} on Euclidean descent [Introduction to linear and nonlinear programming (1973; Zbl 0571.90051)] and complements the work of \textit{J. W. Neuberger} on Sobolev descent [Lect. Notes Math. 564, 341-349 (1976; Zbl 0341.35016)].