##
**ARPACK user’s guide. Solution of large-scale eigenvalue problems with implicitly restarted Arnoldi methods.**
*(English)*
Zbl 0901.65021

Software - Environments - Tools, 6. Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. 142 p. (1998).

This book is a collection of FORTRAN 77 subroutines, designed to solve large scale eigenvalue problems, based on the implicitly restarted Arnoldi method. This software is capable of solving large scale Hermitian, non-Hermitian, standard, or generalized eigenvalue problems from significant application areas. This book, also, explains the acquisition, installation, capabilities, and detailed use of the software for computing desired subset of eigenvalues and eigenvectors of large standard or generalized eigenvalue problems.

This book is divided into five chapters which are followed by three appendices. Chapter 1 gives an overview and contains general information. Chapter 2 provides installation instructions and describes how to get started. Chapter 3 gives a detailed description of how to use all the capabilities of ARPACK. Chapter 4 provides a broad overview of the methods. Chapter 5 discusses implementation and usage details within the main computational routines.

Appendix A provides discussion of the driver routine that is appropriate for their problem. Appendix B: Trace debugging and check pointing are discussed. Appedix C: In this appendix the headers of three main computational routines are exhibited. Information on the calling sequence, input and output parameters, storage and data types is given. Also, error flags and warnings are listed.

The presentation of the material in this book is excellent. Users will be able to better understand the full capabilities of ARPACK and grasp the underlying theory more thoroughly with this book.

This book is divided into five chapters which are followed by three appendices. Chapter 1 gives an overview and contains general information. Chapter 2 provides installation instructions and describes how to get started. Chapter 3 gives a detailed description of how to use all the capabilities of ARPACK. Chapter 4 provides a broad overview of the methods. Chapter 5 discusses implementation and usage details within the main computational routines.

Appendix A provides discussion of the driver routine that is appropriate for their problem. Appendix B: Trace debugging and check pointing are discussed. Appedix C: In this appendix the headers of three main computational routines are exhibited. Information on the calling sequence, input and output parameters, storage and data types is given. Also, error flags and warnings are listed.

The presentation of the material in this book is excellent. Users will be able to better understand the full capabilities of ARPACK and grasp the underlying theory more thoroughly with this book.

Reviewer: P.Narain (Bombay)

### MSC:

65F15 | Numerical computation of eigenvalues and eigenvectors of matrices |

65-02 | Research exposition (monographs, survey articles) pertaining to numerical analysis |

15-04 | Software, source code, etc. for problems pertaining to linear algebra |