Version 1.5.0

3rd January 2012

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HSL_MA74 Unsymmetric full matrix: partial or complete factorization and solution

Given a dense unsymmetric n × n matrix A, HSL_MA74 performs partial factorizations and solutions of corresponding sets of equations. It is designed as a kernel for use in a frontal or multifrontal solver or may be used to factorize and solve a full system of equations.

Eliminations are limited to the leading p n rows and columns. Stability considerations may lead to q p eliminations being performed. The factorization takes the form

PAQ = L1 L2 I D1 A2 U1U2 I ,

where P and Q are permutation matrices, L1 and U1 are unit lower and unit upper triangular matrices of order q, and D1 is the diagonal of order q. The permutation matrices P and Q are of the form

P = P1 I and Q = Q1 I ,

where P1 and Q1 are of order p.

Subroutines are provided for partial solutions, that is, solving systems of the form

L1 L2 I X = B, D1 I X = B, D1 I U1U2 I X = B,

and

U1U2I X = B

and the corresponding equations for a single right-hand side b and solution x.

Subroutines are also provided for partial solutions to transpose systems, that is, solving systems of the form

U1T U2T I X = B, D1 I L1TL 2T I X = B, L1TL 2T I X = B

and the corresponding equations for a single right-hand side b and solution x.

Options are included for threshold partial pivoting, threshold diagonal pivoting, threshold rook pivoting, and static pivoting.

Note: If a full factorization and solution of one or more sets of equations is required (p = n), routines from the LAPACK library may be used (and may be more efficient).