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    Article

    Invariant subspaces for tightly clustered eigenvalues of tridiagonals

    The invariant subspace of a real symmetric tridiagonal matrixT associated with a tight cluster ofm eigenvalues has a special structure. This structure is revealed by the envelope of the subspace (defined in Secti...

    B. N. Parlett in BIT Numerical Mathematics (1996)

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    Chapter

    Accurate Singular Values and Differential QD Algorithms

    In September 1991 J. W. Demmel and W. M. Kahan were awarded the second SIAM prize in numerical linear algebra for their paper ‘Accurate Singular Values of Bidiagonal Matrices’ [1], referred to as DK hereafter....

    K. V. Fernando, B. N. Parlett in Linear Algebra for Large Scale and Real-Time Applications (1993)

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    Chapter

    Implementation Of Lanczos Algorithms on Vector Computers

    We report on two recent studies [17],[18] in which the Lanczos algorithm was transported to a vector machine. The results suggest that our present implementations cannot exploit the full power of Class VI mach...

    B. N. Parlett, B. Nour-Omid, J. Natvig in Supercomputer Applications (1985)

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    Article

    Eigenvector matrices of symmetric tridiagonals

    A simple test is given for determining whether a given matrix is the eigenvector matrix of an (unknown) unreduced symmetric tridiagonal matrix. A list of known necessary conditions is also provided. A lower bo...

    B. N. Parlett, W. -D. Wu in Numerische Mathematik (1984)

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    Article

    Presentation geometrique des methodes de calcul des valeurs propres

    We present a survey of recent work on the convergence of methods for computing eigenvalues and eigenvectors of matrices. We try to maintain a geometric point of view and give pride of place to the γR algorithm.

    B. N. Parlett in Numerische Mathematik (1973)

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    Chapter

    Balancing a Matrix for Calculation of Eigenvalues and Eigenvectors

    This algorithm is based on the work of Osborne [1]. He pointed out that existing eigenvalue programs usually produce results with errors at least of order ε∥A∥ E , where s is the...

    B. N. Parlett, C. Reinsch in Linear Algebra (1971)

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    Chapter

    Balancing a Matrix for Calculation of Eigenvalues and Eigenvectors

    This algorithm is based on the work of Osborne [1]. He pointed out that existing eigenvalue programs usually produce results with errors at least of order ε‖A‖ E , where is the m...

    B. N. Parlett, C. Reinsch in Handbook for Automatic Computation (1971)

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    Article

    The uniform convergence of matrix powers

    M. L. Buchanan, B. N. Parlett in Numerische Mathematik (1966)