Direct Methods for the Solution of Linear Systems
Part of the Texts in Applied Mathematics book series (TAM, volume 37)
A system of m linear equations in n unknowns consists of a set of algebraic relations of the formwhere x j are the unknowns, aij are the coefficients of the system and bi are the components of the right hand side. System (3.1) can be more conveniently written in matrix form aswhere we have denoted by A = (aij) ∈ ℂm×n the coefficient matrix, by b=(bi) ∈ (ℂm the right side vector and by x=(xi) ∈ ℂm the unknown vector, respectively. We call a solution of (3.2) any n-tuple of values xi which satisfies (3.1).
KeywordsLinear System Diagonal Entry Triangular Matrix Cholesky Factorization Sparsity Pattern
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© Springer Science+Business Media New York 2007