Interval Linear Solvers

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Interval Linear Solvers

Intel® MKL provides routines that can be used for solving systems of interval linear equations Ax = b with an interval matrix A =(a_ij) and interval right-hand side vector b =(b_i).

?trtrs solves a triangular system of interval linear equations by backward substitution procedure.
call sitrtrs(uplo, trans, diag, n, nrhs, a, lda, b, ldb, info) call ditrtrs(uplo, trans, diag, n, nrhs, a, lda, b, ldb, info) call crtrtrs(uplo, trans, diag, n, nrhs, a, lda, b, ldb, info) call zrtrtrs(uplo, trans, diag, n, nrhs, a, lda, b, ldb, info) call cctrtrs(uplo, trans, diag, n, nrhs, a, lda, b, ldb, info) call zctrtrs(uplo, trans, diag, n, nrhs, a, lda, b, ldb, info)

?gegas solves a system of interval linear equations by interval Gauss method.
call sigegas(trans, n, nrhs, a, lda, b, ldb, info) call digegas(trans, n, nrhs, a, lda, b, ldb, info) call crgegas(trans, n, nrhs, a, lda, b, ldb, info) call zrgegas(trans, n, nrhs, a, lda, b, ldb, info) call ccgegas(trans, n, nrhs, a, lda, b, ldb, info) call zcgegas(trans, n, nrhs, a, lda, b, ldb, info)

?gehss solves a system of interval linear equations by interval Householder method.
call sigehss(trans, n, nrhs, a, lda, b, ldb, info) call digehss(trans, n, nrhs, a, lda, b, ldb, info)

?gekws solves a system of interval linear equations by Krawczyk iteration method.
call sigekws(trans, n, nrhs, a, lda, b, ldb, epsilon, info) call digekws(trans, n, nrhs, a, lda, b, ldb, epsilon, info) call crgekws(trans, n, nrhs, a, lda, b, ldb, epsilon, info) call zrgekws(trans, n, nrhs, a, lda, b, ldb, epsilon, info) call ccgekws(trans, n, nrhs, a, lda, b, ldb, epsilon, info) call zcgekws(trans, n, nrhs, a, lda, b, ldb, epsilon, info)

?gegss solves a system of interval linear equations by interval Gauss-Seidel method.
call sigegss(trans, n, nrhs, a, lda, b, ldb, encl, epsilon, nits, info) call digegss(trans, n, nrhs, a, lda, b, ldb, encl, epsilon, nits, info) call sigegss(trans, n, nrhs, a, lda, b, ldb, encl, epsilon, nits, info) call digegss(trans, n, nrhs, a, lda, b, ldb, encl, epsilon, nits, info) call sigegss(trans, n, nrhs, a, lda, b, ldb, encl, epsilon, nits, info) call digegss(trans, n, nrhs, a, lda, b, ldb, encl, epsilon, nits, info)

?gehbs solves a system of interval linear equations by Hansen-Bliek-Rohn procedure.
call sigehbs(trans, n, a, lda, b, ldb, info) call digehbs(trans, n, a, lda, b, ldb, info)

?gepps solves a system of interval linear equations by a parameter partitioning method.
call sigepps(trans, n, a, lda, b, ldb, cmpt, mode, estm, epsilon, nits, info) call digepps(trans, n, a, lda, b, ldb, cmpt, mode, estm, epsilon, nits, info)

?gepss solves a system of interval linear equations by a solution partitioning method.
call sigepss(trans, n, a, lda, b, ldb, cmpt, mode, estm, epsilon, nits, info) call digepss(trans, n, a, lda, b, ldb, cmpt, mode, estm, epsilon, nits, info)

?trtri computes inverse interval matrix to a triangular interval matrix.
call sitrtri(uplo, diag, n, a, lda, info) call ditrtri(uplo, diag, n, a, lda, info) call crtrtri(uplo, diag, n, a, lda, info) call zrtrtri(uplo, diag, n, a, lda, info) call cctrtri(uplo, diag, n, a, lda, info) call zctrtri(uplo, diag, n, a, lda, info)

?geszi computes inverse interval matrix to Schulz interval iterative procedure.
call sigeszi(n, a, lda, info) call digeszi(n, a, lda, info)

?gerbr tests regularity of an interval matrix by Ris-Beeck and Rex-Rohn criteria.
call sigerbr(n, a, lda, sr, reg, info) call digerbr(n, a, lda, sr, reg, info)

?gesvr tests regularity/singularity of an interval matrix by Rump and Rex-Rohn singular value criteria.
call sigesvr(n, a, lda, msr, rsr, reg, info) call digesvr(n, a, lda, msr, rsr, reg, info)

?gemip performs midpoint-inverse preconditioning of an interval linear system.
call sigemip(n, nrhs, a, lda, b, ldb, info) call digemip(n, nrhs, a, lda, b, ldb, info) call crgemip(n, nrhs, a, lda, b, ldb, info) call zrgemip(n, nrhs, a, lda, b, ldb, info) call ccgemip(n, nrhs, a, lda, b, ldb, info) call zcgemip(n, nrhs, a, lda, b, ldb, info)