Accession Number : ADA311184

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

Descriptive Note : Technical rept.,

Corporate Author : PITTSBURGH UNIV PA DEPT OF MATHEMATICS AND STATISTICS

Personal Author(s) : Rheinboldt, Werner C.

PDF Url : ADA311184

Report Date : JUL 1996

Pagination or Media Count : 26

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.

Descriptors :   *ALGORITHMS, COMPUTER PROGRAMS, MATHEMATICAL MODELS, COMPUTATIONS, PARAMETERS, MATRICES(MATHEMATICS), FORTRAN, NONLINEAR SYSTEMS, APPROXIMATION(MATHEMATICS), CONVERGENCE, DIFFERENTIAL EQUATIONS, SYSTEMS ANALYSIS, BIFURCATION(MATHEMATICS), NONLINEAR ALGEBRAIC EQUATIONS, MAPPING(TRANSFORMATIONS).

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE