If the matrix is not square, or any of the previous solvers flagsĪ singular or near singular matrix, find a minimum norm solution using.Solve, and perform one refinement iteration using UMFPACK. Hermitian with a real positive diagonal, and the matrix is square, factorize, If the sparse Cholesky factorization failed or the matrix is not.Sparse Cholesky factorization using CHOLMOD. If the matrix is square, Hermitian with a real positive diagonal, attempt.Or lower triangular matrix with row permutations, perform a sparse forward If the matrix is an upper triangular matrix with column permutations.If the matrix is upper or lower triangular perform a sparse forward.if the above failed or the matrix is not Hermitian with a positive.If the matrix is Hermitian with a positive real diagonal, attemptĬholesky factorization using LAPACK xPBTRF.Real diagonal use Gaussian elimination with pivoting using If the above failed or the matrix is not Hermitian with a positive.If the matrix is Hermitian, with a positive real diagonal, attemptĬholesky factorization using LAPACK xPTSV.If the matrix is tridiagonal and the right-hand side is not sparse.Than that given by spparms ('bandden') continue, else goto 4. If the matrix is square, banded and if the band density is less.If the matrix is a permuted diagonal, solve directly taking into.If the matrix is diagonal, solve directly and goto 8.The selection tree for how the linear equation is solve is Re-determined each time it is used in a linear equation. Type is small relative to the cost of factorizing the matrix itself, but inĪny case the matrix type is cached once it is calculated, so that it is not Generally, the cost of determining the matrix The exact solver used to factorize the matrix, depends on the properties Octave includes a polymorphic solver for sparse matrices, where Next: Iterative Techniques Applied to Sparse Matrices, Previous: Creation and Manipulation of Sparse Matrices, Up: Sparse Matrices

Gaussian elimination octave