Abstract and Applied Analysis
Volume 2 (1997), Issue 1-2, Pages 67-72

A convergence result for discreet steepest decent in weighted sobolev spaces

W. T. Mahavier

Mathematics Department, Nicholls State University, P.O. Box 2026, Thibodaux 70310, Louisiana, USA

Received 9 October 1996

Copyright © 1997 W. T. Mahavier. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 David G. Luenberger on Euclidean descent and compliments the work of John W. Neuberger on Sobolev descent.