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Eric Grosse Stanford
A Bjorck Linkoping Sweden and I S Duff Didcot U K
SYSTEMS OF LINEAR EQUATIONS AND APPLICATIONS
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applied approximation assume asymptotic block diagonal bounds CG acceleration Cholesky factor computation condition number conjugate gradient algorithm consider constraints corresponding data structure decomposition defined denote displacement rank dn LCP eigenpair eigenvalue problem eigenvectors elements equivalent example fill-in finite follows Gaussian elimination geodetic given Golub Hence inner iteration inverse iterative methods Lanczos algorithm Lanczos method least squares problems Lemma linear equations linear least squares linear system Math minimize nodes nonlinear nonsingular nonzero normal equations numerical stability obtained operator orthodir orthogonal orthomin orthores P-matrix partitioned permutation piecewise linear pivoting Plemmons positive definite PPP algorithm procedure Proof quadratic programming quotient graph rate of convergence Rayleigh quotient reorthogonalization Ritz satisfies scalar scheme sequence sparse matrix sparsity stabilized step storage subspace symbolic factorization symmetric symmetrizable systems of linear Theorem tion Toeplitz matrices transformations updating upper triangular values variables vector zero