## Large order structural eigenanalysis techniques: algorithms for finite element systems |

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### Contents

Introduction | 9 |

Sparse matrix eigenanalysis | 34 |

Krons dynamic substructuring method | 70 |

Copyright | |

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### Common terms and phrases

analysis applied approximately bandwidth bisection block matrix calculated characteristic roots column composite structure computational effort constraint core space requirements degrees of freedom dot product DSL algorithm DSNCL dynamic stiffness substructuring eigenanalysis eigenproblem eigensolutions of frames eigenvalue problem eigenvalues of frame eigenvectors employed equations of motion finite element frequency full diagonal pivoting Gaussian elimination given Gram-Schmidt hence Householder's method implementation in-core space requirements inverse iteration iteration step Kron Kron matrix Kron-Lanczos Kron's method Lanczos algorithm Lanczos vectors linear located matrix multiplications matrix-vector products mode shapes multiplications expended multiplications required Newton-Raphson procedure non-canonical number of eigenvalues number of iterations number of multiplications obtained operations performed pivotal strategy poles postprocessing stage rate of convergence Rayleigh quotient reduced Ritz eigenvalues scalar shift solution solve sparse matrix stiffness matrices symmetric Table tear coordinates tear points total number transformation trial vectors triangulation tridiagonal matrix zero