Matrix inverse

The inverse of a scalar matrix may be used by using the Inverse function of the BIAS/Profil package or with

 
void ALIAS_MRINVD(VECTOR &A,VECTOR &B,int N,int *KOD,double *DET,double EPS,
                  INTEGER_VECTOR &IL,INTEGER_VECTOR &IC)

where

• A is the matrix given by column
• B is the inverse of A
• N is the dimension of the matrix
• KOD is a return code. If KOD is 0 then A is estimated not to have an inverse, otherwise KOD is set to 1
• DET: the determinant of A
• EPS: a threshold, if a pivot has an abolute value less than this value, then it is assumed to be 0
• IL, IC: working table of size N

The inverse of an interval matrix may be defined as the set of matrices corresponding to the inverse of a matrix included in the set defined by the interval matrix. This set cannot usually be computed exactly but a set of matrices guaranteed to include the inverse interval matrix may be computed. The following procedure allows one to compute such overestimation.

 
int Inverse_Interval_Matrix(int Dim,int cond,INTERVAL_MATRIX &Jac,INTERVAL_MATRIX &InvJac)

where Dim is the dimension of the matrix Jac. The flag cond has to be set to 1 if pre-conditioning is used, 0 otherwise. Pre-conditionning will usually leads to a smaller overestimation but is more computer intensive. This procedures returns 1 if it has been able to compute the inverse, 0 otherwise.

Note that using this procedure should not be used for solving an interval linear system.