## Chebyshev, Krylov, Lanczos: matrix relationship and computationsStanford University, 1989 - 252 pages |

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### Contents

Calculating Orthogonal Polynomials | 11 |

Moments and matrices | 24 |

Block generalizations | 44 |

Copyright | |

7 other sections not shown

### Common terms and phrases

Bairstow's method basis polynomials Bibliographic notes block Krylov sequence block Lanczos algorithm block vector Chapter characteristic polynomial Cholesky factor coefficients companion matrix computed comrade matrix condition number consider convergence CSI method Danilewski algorithm deflation derived determine diagonal elements distribution dk,k+i eigenvalue calculations eigenvalue problem eigenvectors equations error extreme eigenvalues functions Gene Golub Gragg Hence Hessenberg form Hessenberg matrix initial values initial vector inner product input matrix iterative methods Krylov matrix Krylov method Laguerre's method Lanczos polynomials matrix-valued polynomials minimum polynomial modified Chebyshev algorithm modified moments monic n x n non-derogatory non-zero nonsingular nonsymmetric numerical obtain optimal parameters ordinary moments orthogonal polynomials orthonormal p x p Parlett pivot polynomial bases power basis presented QR algorithm quadratic recurrence relation root finders satisfy a three-term scalar similarity transformation sub-diagonal submatrix subspace symmetric Lanczos algorithm symmetric matrix thesis three-term recurrence relation tridiagonal form tridiagonal matrix unreduced zero