Algorithms for Nonlinear Equations

Abstract

This project involved research in three areas: Mathematical software, globally convergent homotopy methods, and hybrid quasi-Newton algorithms for large scale structural Optimization. The homotopy research, concerned mainly with low dimensional ferociously nonlinear problems, centered on proving convergence theorems, devising homotopy curve tracking algorithms, and development of the mathematical software package Homopack. The structural optimization research concerned optimization algorithms for very large sparse nonlinear problems, where maintaining sparsity is absolutely necessary and even matrix multiples are costly. Structural optimization and equilibrium configuration computation via quasi-Newton and homotopy techniques require entirely different technology for quasi-Newton and homotopy algorithms, using realistic test problems from structural mechanics.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1988
Accession Number
ADA205073

Entities

People

  • Layne T. Watson

Organizations

  • Virginia Tech

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Availability
  • Boundary Value Problems
  • Digital Signal Processing
  • Equations
  • Flow
  • Fluid Mechanics
  • Heat Transfer
  • Linear Algebra
  • Magnetic Fields
  • Mathematical Programming
  • Mechanics
  • Optimization
  • Polynomials
  • Signal Processing
  • Structural Mechanics
  • Teamwork

Readers

  • Operations Research