The Combined Schubert/Secant Finite-Difference Algorithm for Solving Sparse Nonlinear Systems of Equations

Abstract

This paper presents an algorithm the combined Schubert/secant/finite difference algorithm, for solving sparse nonlinear systems of equations. This algorithm is based on dividing the columns of the Jacobian into two parts, and using different algorithms on each part. This algorithm incorporates advantages of both algorithms by exploiting some special structure of the Jacobian to obtain a good approximation to the Jacobian by using as little effort as possible. Kantorovich-type analysis and a locally q-superlinear convergence result for this algorithm are given.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1986
Accession Number
ADA453834

Entities

People

  • Guangye Li
  • J. E. Dennis Jr.

Organizations

  • Rice University

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Applied Mathematics
  • Equations
  • Information Operations
  • Mathematics
  • Nonlinear Systems

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Operations Research