## Matrix Computation and Mathematical SoftwareLinear algebra background; types and sources of matrix computational problems; type of matrix that arise; gauss elimination and LU factorization; mathematical software objectives; mathematical software performance evaluation; how do you know you have right answers?; conditioning and backward error analysis; iterative methods; linear least squares and regression; projects; standard linear algebra software. |

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### Contents

Linear Algebra Background | 5 |

Types and Sources of Matrix | 17 |

Types of Matrices That Arise | 25 |

Copyright | |

15 other sections not shown

### Common terms and phrases

Aird-Lynch algorithm approximate solution arithmetic array backward error analysis band matrix basic BLAS calculation calling sequence Chapter column compiler convergence decomposition differential equation digits dimension dot product double precision efficiency eigenvalues elements equations Ax error estimator evaluation example factor Fortran Gauss elimination Gauss-Seidel Gram-Schmidt hand side Hilbert matrix IDGT implementation IMSL INCX INCY input INTEGER inverse iterative improvement iterative methods Jacobi method least squares problem least-squares LEQT1B library program linear algebra linear equation solver linear equations linear system LINPACK lower triangular mathematical software matrix computation multiply nonzero norm obtain operations orthogonal parameters partial pivoting performance profiles permutation permutation matrix perturbations positive definite Prob RCOND residual right-hand side round-off errors routine SGECO SGEFA SGESL Show singular value decomposition solution of Ax solve Ax Space economizer solution storage mode subprograms subroutines symmetric system of equations tion triangular matrix uncertainty upper triangular variables vector zero