Keyword : Symmetric

 F01ABF Inverse of real symmetric positive definite matrix using iterative refinement F01ADF Inverse of real symmetric positive definite matrix F01EDF Real symmetric matrix exponential F01EFF Function of a real symmetric matrix F01MCF $LD{L}^{\mathrm{T}}$ factorization of real symmetric positive definite variable-bandwidth matrix F02FJF Selected eigenvalues and eigenvectors of sparse symmetric eigenproblem (Black Box) F03BFF Determinant of real symmetric positive definite matrix F03BHF Determinant of real symmetric positive definite banded matrix F04ABF Solution of real symmetric positive definite simultaneous linear equations with multiple right-hand sides using iterative refinement (Black Box) F04ASF Solution of real symmetric positive definite simultaneous linear equations, one right-hand side using iterative refinement (Black Box) F04BDF Computes the solution and error-bound to a real symmetric positive definite system of linear equations F04BEF Computes the solution and error-bound to a real symmetric positive definite system of linear equations, packed storage F04BFF Computes the solution and error-bound to a real symmetric positive definite banded system of linear equations F04BGF Computes the solution and error-bound to a real symmetric positive definite tridiagonal system of linear equations F04BHF Computes the solution and error-bound to a real symmetric system of linear equations F04BJF Computes the solution and error-bound to a real symmetric system of linear equations, packed storage F04DHF Computes the solution and error-bound to a complex symmetric system of linear equations F04DJF Computes the solution and error-bound to a complex symmetric system of linear equations, packed storage F04FEF Solution of the Yule–Walker equations for real symmetric positive definite Toeplitz matrix, one right-hand side F04FFF Solution of real symmetric positive definite Toeplitz system, one right-hand side F04MCF Solution of real symmetric positive definite variable-bandwidth simultaneous linear equations (coefficient matrix already factorized by F01MCF) F04MEF Update solution of the Yule–Walker equations for real symmetric positive definite Toeplitz matrix F04MFF Update solution of real symmetric positive definite Toeplitz system F06BHF Apply real similarity rotation to 2 by 2 symmetric matrix F06BPF Compute eigenvalue of 2 by 2 real symmetric matrix F06FPF Apply real symmetric plane rotation to two vectors F06PCF Matrix-vector product, real symmetric matrix F06PDF Matrix-vector product, real symmetric band matrix F06PEF Matrix-vector product, real symmetric packed matrix F06PPF Rank-1 update, real symmetric matrix F06PQF Rank-1 update, real symmetric packed matrix F06PRF Rank-2 update, real symmetric matrix F06PSF Rank-2 update, real symmetric packed matrix F06QMF Orthogonal similarity transformation of real symmetric matrix as a sequence of plane rotations F06RCF $1$-norm, $\infty$-norm, Frobenius norm, largest absolute element, real symmetric matrix F06RDF $1$-norm, $\infty$-norm, Frobenius norm, largest absolute element, real symmetric matrix, packed storage F06REF $1$-norm, $\infty$-norm, Frobenius norm, largest absolute element, real symmetric band matrix F06RPF $1$-norm, $\infty$-norm, Frobenius norm, largest absolute element, real symmetric tridiagonal matrix F06TAF Matrix-vector product, complex symmetric matrix F06TBF Rank-1 update, complex symmetric matrix F06TCF Matrix-vector product, complex symmetric packed matrix F06TDF Rank-1 update, complex symmetric packed matrix F06UFF $1$-norm, $\infty$-norm, Frobenius norm, largest absolute element, complex symmetric matrix F06UGF $1$-norm, $\infty$-norm, Frobenius norm, largest absolute element, complex symmetric matrix, packed storage F06UHF $1$-norm, $\infty$-norm, Frobenius norm, largest absolute element, complex symmetric band matrix F06WAF 1-norm, $\infty$-norm, Frobenius norm, largest absolute element, real symmetric matrix, Rectangular Full Packed format F06WCF Rank-$k$ update of a real symmetric matrix, Rectangular Full Packed format F06WQF Rank-$k$ update of a complex Hermitian matrix, Rectangular Full Packed format F06YCF Matrix-matrix product, one real symmetric matrix, one real rectangular matrix F06YPF Rank-$k$ update of a real symmetric matrix F06YRF Rank-$2k$ update of a real symmetric matrix F06ZTF Matrix-matrix product, one complex symmetric matrix, one complex rectangular matrix F06ZUF Rank-$k$ update of a complex symmetric matrix F06ZWF Rank-$2k$ update of a complex symmetric matrix F07FBF Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite system of linear equations F07FCF Uses the Cholesky factorization to compute the solution for a real symmetric positive definite system of linear equations F07FDF Cholesky factorization of real symmetric positive definite matrix F07FEF Solution of real symmetric positive definite system of linear equations, multiple right-hand sides, matrix already factorized by F07FDF F07FFF Computes row and column scalings intended to equilibrate a real symmetric positive definite matrix and reduce its condition number F07FGF Estimate condition number of real symmetric positive definite matrix, matrix already factorized by F07FDF F07FHF Refined solution with error bounds of real symmetric positive definite system of linear equations, multiple right-hand sides F07FJF Inverse of real symmetric positive definite matrix, matrix already factorized by F07FDF F07GAF Computes the solution to a real symmetric positive definite system of linear equations, packed storage F07GBF Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite system of linear equations, packed storage F07GDF Cholesky factorization of real symmetric positive definite matrix, packed storage F07GEF Solution of real symmetric positive definite system of linear equations, multiple right-hand sides, matrix already factorized by F07GDF, packed storage F07GFF Computes row and column scalings intended to equilibrate a real symmetric positive definite matrix and reduce its condition number, packed storage F07GGF Estimate condition number of real symmetric positive definite matrix, matrix already factorized by F07GDF, packed storage F07GHF Refined solution with error bounds of real symmetric positive definite system of linear equations, multiple right-hand sides, packed storage F07GJF Inverse of real symmetric positive definite matrix, matrix already factorized by F07GDF, packed storage F07HAF Computes the solution to a real symmetric positive definite banded system of linear equations F07HBF Uses the Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite banded system of linear equations F07HDF Cholesky factorization of real symmetric positive definite band matrix F07HEF Solution of real symmetric positive definite band system of linear equations, multiple right-hand sides, matrix already factorized by F07HDF F07HFF Computes row and column scalings intended to equilibrate a real symmetric positive definite banded matrix and reduce its condition number F07HGF Estimate condition number of real symmetric positive definite band matrix, matrix already factorized by F07HDF F07HHF Refined solution with error bounds of real symmetric positive definite band system of linear equations, multiple right-hand sides F07JAF Computes the solution to a real symmetric positive definite tridiagonal system of linear equations F07JBF Uses the modified Cholesky factorization to compute the solution, error-bound and condition estimate for a real symmetric positive definite tridiagonal system of linear equations F07JDF Computes the modified Cholesky factorization of a real symmetric positive definite tridiagonal matrix F07JEF Solves a real symmetric positive definite tridiagonal system using the modified Cholesky factorization computed by F07JDF F07JGF Computes the reciprocal of the condition number of a real symmetric positive definite tridiagonal system using the modified Cholesky factorization computed by F07JDF F07JHF Refined solution with error bounds of real symmetric positive definite tridiagonal system of linear equations, multiple right-hand sides F07KDF Cholesky factorization of real symmetric positive semidefinite matrix F07MAF Computes the solution to a real symmetric system of linear equations F07MBF Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations F07MDF Bunch–Kaufman factorization of real symmetric indefinite matrix F07MEF Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07MDF F07MGF Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07MDF F07MHF Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides F07MJF Inverse of real symmetric indefinite matrix, matrix already factorized by F07MDF F07NRF Bunch–Kaufman factorization of complex symmetric matrix F07NSF Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by F07NRF F07NUF Estimate condition number of complex symmetric matrix, matrix already factorized by F07NRF F07NVF Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides F07NWF Inverse of complex symmetric matrix, matrix already factorized by F07NRF F07PAF Computes the solution to a real symmetric system of linear equations, packed storage F07PBF Uses the diagonal pivoting factorization to compute the solution to a real symmetric system of linear equations, packed storage F07PDF Bunch–Kaufman factorization of real symmetric indefinite matrix, packed storage F07PEF Solution of real symmetric indefinite system of linear equations, multiple right-hand sides, matrix already factorized by F07PDF, packed storage F07PGF Estimate condition number of real symmetric indefinite matrix, matrix already factorized by F07PDF, packed storage F07PHF Refined solution with error bounds of real symmetric indefinite system of linear equations, multiple right-hand sides, packed storage F07PJF Inverse of real symmetric indefinite matrix, matrix already factorized by F07PDF, packed storage F07QNF Computes the solution to a complex symmetric system of linear equations, packed storage F07QPF Uses the diagonal pivoting factorization to compute the solution to a complex symmetric system of linear equations, packed storage F07QRF Bunch–Kaufman factorization of complex symmetric matrix, packed storage F07QSF Solution of complex symmetric system of linear equations, multiple right-hand sides, matrix already factorized by F07QRF, packed storage F07QUF Estimate condition number of complex symmetric matrix, matrix already factorized by F07QRF, packed storage F07QVF Refined solution with error bounds of complex symmetric system of linear equations, multiple right-hand sides, packed storage F07QWF Inverse of complex symmetric matrix, matrix already factorized by F07QRF, packed storage F07WDF Cholesky factorization of real symmetric positive definite matrix, Rectangular Full Packed format F07WEF Solution of real symmetric positive definite system of linear equations, multiple right-hand sides, coefficient matrix already factorized by F07WDF, Rectangular Full Packed format F07WJF Inverse of real symmetric positive definite matrix, matrix already factorized by F07WDF, Rectangular Full Packed format F08FAF Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix F08FBF Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix F08FCF Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix (divide-and-conquer) F08FDF Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix (Relatively Robust Representations) F08FEF Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form F08FLF Computes the reciprocal condition numbers for the eigenvectors of a real symmetric or complex Hermitian matrix or for the left or right singular vectors of a general matrix F08FSF Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form F08GAF Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage F08GBF Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric matrix, packed storage F08GCF Computes all eigenvalues and, optionally, all eigenvectors of real symmetric matrix, packed storage (divide-and-conquer) F08GEF Orthogonal reduction of real symmetric matrix to symmetric tridiagonal form, packed storage F08GSF Unitary reduction of complex Hermitian matrix to real symmetric tridiagonal form, packed storage F08HAF Computes all eigenvalues and, optionally, eigenvectors of a real symmetric band matrix F08HBF Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix F08HCF Computes all eigenvalues and, optionally, all eigenvectors of real symmetric band matrix (divide-and-conquer) F08HEF Orthogonal reduction of real symmetric band matrix to symmetric tridiagonal form F08HSF Unitary reduction of complex Hermitian band matrix to real symmetric tridiagonal form F08JBF Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix F08JCF Computes all eigenvalues and, optionally, all eigenvectors of real symmetric tridiagonal matrix (divide-and-conquer) F08JDF Computes selected eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix (Relatively Robust Representations) F08JEF All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from real symmetric matrix using the implicit $QL$ or $QR$ algorithm F08JFF All eigenvalues of real symmetric tridiagonal matrix, root-free variant of the $QL$ or $QR$ algorithm F08JGF Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from real symmetric positive definite matrix F08JHF Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a matrix reduced to this form (divide-and-conquer) F08JJF Selected eigenvalues of real symmetric tridiagonal matrix by bisection F08JKF Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in real array F08JLF Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a symmetric matrix reduced to this form (Relatively Robust Representations) F08JSF All eigenvalues and eigenvectors of real symmetric tridiagonal matrix, reduced from complex Hermitian matrix, using the implicit $QL$ or $QR$ algorithm F08JUF Computes all eigenvalues and eigenvectors of real symmetric positive definite tridiagonal matrix, reduced from complex Hermitian positive definite matrix F08JVF Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (divide-and-conquer) F08JXF Selected eigenvectors of real symmetric tridiagonal matrix by inverse iteration, storing eigenvectors in complex array F08JYF Computes all eigenvalues and, optionally, eigenvectors of a real symmetric tridiagonal matrix or a complex Hermitian matrix reduced to this form (Relatively Robust Representations) F08UFF Computes a split Cholesky factorization of real symmetric positive definite band matrix $A$ F11GDF Real sparse symmetric linear systems, setup for F11GEF F11GEF Real sparse symmetric linear systems, preconditioned conjugate gradient or Lanczos method or the MINRES algorithm F11GFF Real sparse symmetric linear systems, diagnostic for F11GEF F11JAF Real sparse symmetric matrix, incomplete Cholesky factorization F11JCF Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, preconditioner computed by F11JAF (Black Box) F11JDF Solution of linear system involving preconditioning matrix generated by applying SSOR to real sparse symmetric matrix F11JEF Solution of real sparse symmetric linear system, conjugate gradient/Lanczos method, Jacobi or SSOR preconditioner (Black Box) F11XEF Real sparse symmetric matrix vector multiply F11ZBF Real sparse symmetric matrix reorder routine

© The Numerical Algorithms Group Ltd, Oxford UK. 2013