Numerical Mathematics pp 57-122 | Cite as

# Direct Methods for the Solution of Linear Systems

Chapter

## Abstract

A system of where where we have denoted by A = (a

*m*linear equations in n unknowns consists of a set of algebraic relations of the form(3.1)

*x*_{ j}are the unknowns,*a*_{ij}are the coefficients of the system and b_{i}are the components of the right hand side. System (3.1) can be more conveniently written in matrix form as(3.2)

_{ij}) ∈ ℂ^{m×n}the coefficient matrix, by b=(b_{i}) ∈ (ℂ^{m}the right side vector and by x=(x_{i}) ∈ ℂ^{m}the unknown vector, respectively. We call a*solution*of (3.2) any n-tuple of values*x*_{i}which satisfies (3.1).## Keywords

Linear System Diagonal Entry Triangular Matrix Cholesky Factorization Sparsity Pattern
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer Science+Business Media New York 2007