f04mcf

f04mcf © Numerical Algorithms Group, 2002.

Purpose

F04MCF Approximate solution of real symmetric positive-definite variable-bandwidth simultaneous linear equations (coefficient matrix already factorized)

Synopsis

[x,ifail] = f04mcf(al,d,nrow,b<,iselct,ifail>)

Description

 
 The normal use of this routine is the solution of the systems 
 AX=B, following a call of F01MCF to determine the Cholesky 
                    T                                   
 factorization A=LDL  of the symmetric positive-definite variable-
 bandwidth matrix A.
 
 However, the routine may be used to solve any one of the 
 following systems of linear algebraic equations:
 
         T  
 (1)  LDL X = B (usual system),
 
 (2)  LDX   = B (lower triangular system),
 
        T   
 (3)  DL X  = B (upper triangular system),
 
        T                                                          
 (4)  LL X  = B                                                    
 
 (5)  LX    = B (unit lower triangular system),
 
       T    
 (6)  L X   = B (unit upper triangular system).
 
 L denotes a unit lower triangular variable-bandwidth matrix of 
 order n, D a diagonal matrix of order n, and B a set of right-
 hand sides.
 
 The matrix L is represented by the elements lying within its 
 envelope i.e., between the first non-zero of each row and the 
 diagonal. The width NROW(i) of the ith row is the number of 
 elements between the first non-zero element and the element on 
 the diagonal inclusive.

Parameters

f04mcf

Required Input Arguments:

al (:)                                real
d (:)                                 real
nrow (:)                              integer
b (:,:)                               real

Optional Input Arguments:                       <Default>

iselct                                integer  1
ifail                                 integer  -1

Output Arguments:

x (:,:)                               real
ifail                                 integer