Many applications in science and engineering require the solution of a system of linear equations. This problem is usually expressed mathematically by the matrix-vector equation,

Ax

=

b

, where

A

is an

m

-by-

n

matrix,

x

is the

n

element column vector and

b

is the

m

element column vector. The matrix

A

is usually referred to as the coefficient matrix, and the vectors

x

and

b

are referred to as the solution vector and the right-hand side, respectively.

Basic concepts related to solving linear systems with sparse matrices are described in Sparse Linear Systems and various storage schemes for sparse matrices are described in Sparse Matrix Storage Formats.