## LAPACK Users' Guide: Third EditionE. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammerling, A. McKenney, D. Sorensen LAPACK is a library of numerical linear algebra subroutines designed for high performance on workstations, vector computers, and shared memory multiprocessors. Release 3.0 of LAPACK introduces new routines and extends the functionality of existing routines. The most significant new routines and functions include: 1. a faster singular value decomposition computed by divide-and-conquer 2. faster routines for solving rank-deficient least squares problems: Using QR with column pivoting using the SVD based on divide-and-conquer 3. new routines for the generalized symmetric eigenproblem: faster routines based on divide-and-conquer routines based on bisection/inverse iteration, for computing part of the spectrum 4. faster routine for the symmetric eigenproblem using "relatively robust eigenvector algorithm" 5. new simple and expert drivers for the generalized nonsymmetric eigenproblem, including error bounds 6. solver for generalized Sylvester equation, used in 5 7.computational routines used in 5 Each Users' Guide comes with a 'Quick Reference Guide' card. |

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### Contents

Essentials | 3 |

Contents of LAPACK | 9 |

Performance of LAPACK | 54 |

Accuracy and Stability | 77 |

Documentation and Software Conventions | 134 |

Installing LAPACK Routines | 145 |

A Index of Driver and Computational Routines | 156 |

B Index of Auxiliary Routines | 169 |

Converting from LINPACK or EISPACK | 185 |

383 | |

397 | |

### Common terms and phrases

approximate error band matrix bidiagonal blocked algorithm bO bO Cholesky factorization columns Computational routines condition number CQ CQ diagonal Double precision driver routines eigenvalue problem eigenvalues and eigenvectors EISPACK EPSMCH error bounds expert driver IBM Power IWORK LAPACK routines least squares problem linear least squares LINPACK matrix pair megaflops netlib norm orthogonal orthogonal/unitary packed storage performance positive definite QR factorization RCOND real complex real symmetric simple driver singular value decomposition singular vectors Solves symmetric matrix symmetric/Hermitian system of linear tridiagonal matrix UPLO upper triangular