Interval Linear Solvers

# Interval Linear Solvers

Intel® MKL Interval Linear solver routines can be used for:

- solving systems of interval linear equations `Ax = b` with an interval matrix `A = ( aij)` and interval right-hand side vector `b = ( bi)`;

- checking properties of interval matrices.

For more information on key concepts of interval linear systems, see Appendix “Linear Solvers Basics”.

Routines described below are subdivided according to the problems they solve into the following groups:

Routines for Fast Solution of Interval Systems

Routines for Sharp Solution of Interval Systems

Routines for Inverting Interval Matrices

Routines for Checking Properties of Interval Matrices

Auxiliary and Utility Routines

Table “Intel MKL Interval Linear Solver Routines” contains the full list of Intel MKL routines for solving interval linear systems.

Intel MKL Interval Linear Solver Routines
Routine Name | Description
--- | ---
?trtrs | Solves a triangular system of interval linear equations by backward substitution procedure.
?gegas | Solves a system of interval linear equations by interval Gauss method.
?gehss | Solves a system of interval linear equations by interval Householder method.
?gekws | Solves a system of interval linear equations by Krawczyk iteration method.
?gegss | Solves a system of interval linear equations by interval Gauss-Seidel iteration.
?gehbs | Solves a system of interval linear equations by Hansen-Bliek-Rohn procedure.
?gepps | Solves a system of interval linear equations by a parameter partitioning method.
?gepss | Solves a system of interval linear equations by a solution partitioning method.
?trtri | Computes inverse interval matrix to a triangular interval matrix.
?geszi | Computes inverse interval matrix by Schulz interval iterative procedure.
?gerbr | Tests regularity of an interval matrix by Ris-Beeck and Rex-Rohn criteria
?gesvr | Tests regularity/singularity of an interval matrix by Rump and Rex-Rohn singular value criteria.
?gemip | Performs midpoint-inverse preconditioning of an interval linear system.