Numerical computation of the sign of the determinant with additive and multiplicative preconditionin...

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" Numerical computation of the sign of the determinant with additive and multiplicative preconditioning "
Islam A. T. F. Taj-Eddin V. Y. Pan

Document Type	:	Latin Dissertation
Language of Document	:	English
Record Number	:	55048
Doc. No	:	TL25002
Call number	:	‭3283756‬
Main Entry	:	Islam A. T. F. Taj-Eddin
Title & Author	:	Numerical computation of the sign of the determinant with additive and multiplicative preconditioning\ Islam A. T. F. Taj-Eddin
College	:	City University of New York
Date	:	2007
Degree	:	Ph.D.
student score	:	2007
Page No	:	72
Abstract	:	Accurate computation of the sign and the value of a matrix determinant attracts a great deal of attention. Various algebraic and geometric computations boil down to it. This includes the computation of a convex hull and a Voronoi diagram as well as the evaluation and expansion of scalar, univariate and multivariate resultants. In the present day computing environment, it is most effective to compute determinants numerically with IEEE standard double precision floating-point numbers provided rounding errors are controlled. That control is difficult where the input matrix is ill conditioned but easy where the matrix is well conditioned. This motivates the application of preconditioning methods. In this thesis, recent techniques of additive preconditioning are applied, the technicalities of this application are elaborated, and the power of the approach is demonstrated with numerical experiments.
Subject	:	Communication and the arts; Applied sciences; Additive preconditioning; Matrix determinants; Multiplicative preconditioning; Numerical computation; Voronoi diagrams; Information systems; Operations research; Computer science; 0984:Computer science; 0723:Information systems; 0796:Operations research
Added Entry	:	V. Y. Pan
Added Entry	:	City University of New York