## Contributions to the Solution of Systems of Linear Equations and the Determination of Eigenvalues |

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### Contents

Practical solution of linear equations and inversion | 1 |

Punchedcard experiments with accelerated gradient methods | 55 |

Iterative methods of solving linear problems on Hilbert space | 71 |

3 other sections not shown

### Common terms and phrases

a a a a acceleration step apply back-substitution bounded CM CM coefficients column-by-column multiplication completely continuous complex numbers computation conjugate gradient consider convergence Corollary corresponding Crout defined denote diagonal elements diagonal matrix disks eigenvalues eigenvectors elimination equivalent error example exists expanding subspaces f(xk follows function geometric geometric progression given Hence Hermitian matrix Hestenes Hilbert matrix Hilbert space implies inequality initial vector inner product integral inverse involving iterative procedures Legendre operator lemma linear equations linear operator linear subspace lower triangular matrix Math minimizes F(x nonnegative nonsingular normal matrix nxn matrix obtained optimum gradient method optimum gradient steps orthogonal Ostrowski's theorem Ov CM positive definite operator positive numbers problem PROOF properties recorded row sums row-by-row multiplication satisfy selfadjoint sequence of expanding steps and accelerate subspace SB symmetric matrix Taussky theorem 1.2 tion triangular resolution unit triangle vectors Wielandt zero