Generalized Capacitance Matrix Theorems for Solving Linear Systems 1
نویسندگان
چکیده
The capacitance matrix method has been widely used as an e cient 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 A 2 <n n and U;V 2 <n p. Extensions to the capacitance matrix method with restrictive assumptions on the matrices A and (A+UVT ) have been reported in the past. In this paper, we present several theorems which are generalizations of the capacitance matrix theorem [2] and are suited for very general matrices A and (A+UVT ). A modi ed capacitance matrix method is developed from these theorems and holds the promise of being applicable to more general boundary value problems; in addition, it gives ample freedom to choose the matrix A for developing very e cient numerical algorithms.
منابع مشابه
Generalized Capacitance Matrix Theorems and Algorithm for Solving Linear Systems
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 + UV ) with A ∈ <n×n and U,V ∈ <n×p. Extensions of this method reported in literature have made restrictive assumptions on the matr...
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