Manpack: A Set of Algorithms for Computations on Implicitly Defined Manifolds.

Abstract

Mathematical models often involve differentiable manifolds that are implicitly defined as the solution sets of systems of nonlinear equations. The resulting computational tasks differ considerably from those arising for manifolds defined in parametric form. Here a collection of algorithms is presented for performing a range of essential tasks on general, implicitly specified submanifolds of a finite dimensional space. This includes algorithms for determining local parametrizations and their derivatives, and for evaluating quantities related to the curvature and with sensitivity measures. The methods have been implemented as a FORTRAN 77 package, called MANPAK.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1996
Accession Number
ADA311184

Entities

People

  • Werner Rheinboldt

Organizations

  • University of Pittsburgh

Tags

Communities of Interest

  • Autonomy

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Computational Science
  • Computations
  • Computer Science
  • Coordinate Systems
  • Curvature
  • Differential Equations
  • Differential Geometry
  • Equations
  • Geometric Forms
  • Geometry
  • Mathematical Models
  • Mathematics
  • Numerical Analysis
  • Sensitivity
  • Theorems

Readers

  • Computational Modeling and Simulation
  • Graph Algorithms and Convex Optimization.
  • Operations Research

Technology Areas

  • Space