Matrix Computations 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. |
Common terms and phrases
accuracy Aird-Lynch answer approximate arithmetic array b₁ b₂ backward error analysis band matrix calculation Chap chapter coefficients column compiler composite error estimator consider convergence differential equation dimension dot product double precision efficiency eigenvalues elements EPSA evaluation example execution factor feature space Fortran Gauss elimination Gauss-Seidel Hilbert matrix ill-conditioned INCX input inverse iterative improvement iterative methods Jacobi method least-squares library program linear algebra linear equation solver linear equations linear system LINPACK lower triangular mathematical software matrix computation multiply nonzero norm obtain operations original problem orthogonal P₁ parameters partial pivoting performance profile permutation matrix perturbations polynomial positive definite Prob problem space residual right-hand side round-off errors routine Show singular situation solution of Ax solving Ax standard condition number subprograms subroutine symmetric systems of equations tion true solution uncertainty upper triangular values variables vector versus x₁ zero