NDLI: Generalized Capacitance Matrix Theorems and Algorithm for Solving Linear Systems

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Lai, Shang-Hong Vemuri, Baba C.
Copyright Year	1998
Abstract	The capacitance matrix method has been widely used as an efficient numerical tool for solving the boundary value problems on irregular regions. Initially, this method was based on the Sherman--Morrison--Woodbury formula, an expression for the inverse of the matrix (A+UVT) with ${\bf A} \in \Re^{n \times n}$ and ${\bf U, V} \in \Re^{n \times p}$. Extensions of this method reported in literature have made restrictive assumptions on the matrices A and (A+UVT). In this paper, we present several theorems which are generalizations of the capacitance matrix theorem in \cite{Buzbee} and are suited for very general matrices A and (A +UVT). A generalized capacitance matrix algorithm is developed from these theorems and holds the promise of being applicable to more general problems; in addition, it gives ample freedom to choose the matrix A for developing very efficient numerical algorithms. We demonstrate the usefulness of our generalized capacitance matrix algorithm by applying it to efficiently solve large sparse linear systems in several computer vision problems, namely, the surface reconstruction and interpolation, and the shape from orientation problem.
Starting Page	1024
Ending Page	1045
Page Count	22
File Format	PDF
ISSN	10648275
DOI	10.1137/S1064827595283653
e-ISSN	10957197
Issue Number	3
Volume Number	19
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-25
Access Restriction	Subscribed
Subject Keyword	surface interpolation Solution of discretized equations shape from orientation early vision Iterative methods for linear systems Direct methods for linear systems and matrix inversion surface reconstruction capacitance matrix algorithms
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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