LAPACK Users' Guide / Edition 2

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Since its initial release in February 1992, LAPACK has expanded in both depth and breadth. LAPACK is now available in both Fortran and C. The publication of this second edition of the Users' Guide coincides with the release of version 2.0 of the LAPACK software.

This release of LAPACK introduces new routines and extends the functionality of existing routines. Prominent among the new routines are driver and computational routines for the generalized nonsymmetric eigenproblem, generalized linear least squares problems, the generalized singular value decomposition, a generalized symmetric-definite eigenproblem, and divide-and-conquer methods for symmetric eigenproblems. Additional computational routines include the generalized QR and RQ factorization and reduction of a band matrix to bidiagonal form.

The following are some of the additional modifications made since publication of the first edition:

  • a description of LAPACK-related software projects has been added
  • a new LAPACK benchmark section has been added that gives performance numbers for selected LAPACK routines
  • the chapter on accuracy and stability has been simplified and expanded, separating the theory and details from the descriptions
  • all of the new routines have been added to the following appendices: Index of Driver and Computational Routines; Index of Auxiliary Routines; Converting from LINPACK or EISPACK
  • the new notes written during the LAPACK2 and ScaLAPACK projects have been added
  • the Specifications of Routines section has been expanded and updated to include the new routines and revisions to the existing routines
  • the bibliography has been expanded
  • the index has been separated into one for key words and another for routines
  • tables have been added to show the performance for specific routines

If you are familiar with the first edition of this book, you will want to update your library. If you have been reluctant to switch to LAPACK, the LAPACK Users' Guide, Second Edition will help you facilitate this change.

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Editorial Reviews

Coinciding with the release of version 3.0 of the LAPACK software, this guide includes updated information on accessing LAPACK and related projects via the Web; coverage of the new routines; updated performance results; and an expanded section on accuracy and stability that includes error bounds for generalized least squares. Annotation c. Book News, Inc., Portland, OR (
Studies In Informatics and Control
LAPACK is more than a successor to LINPACK and EISPACK; it extends the functional capacity of these packages by including equilibration, iterative refinement, error bounds, and driver routines for linear systems, routines for computing and re-ordering the Schur factorization, and condition estimation routines for eigenvalue problems. .The underlying philosophy of LAPACK as well as a detailed description of its usage are exposed in the LAPACK Users' Guide . Specifically, this guide gives an informal introduction to the design of the algorithms and software, summarizes the contents of the package, describes conventions used in the software and its documentation, and includes complete specifications for calling the driver and computational routines.
— Vol. 4, No. 4, December 1995
Xiao-Chuan Cai
As a successor to the software packages LINPACK and EISPACK, LAPACK provides more efficient and accurate routines for the solutions of dense systems of linear equations, lest squares problems, eigenvalue and singular value problems. .Overall, this is a well-written book, and I highly recommend it to those who are new to LAPACK or are interested in understanding or using the new routines released in version 2.0 of LAPACK.
Mathematics of Computation, Vol. 65, Number 216 October 1996.
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Product Details

  • ISBN-13: 9780898713459
  • Publisher: SIAM
  • Publication date: 1/28/1995
  • Series: Miscellaneous Bks.
  • Edition number: 2
  • Pages: 325

Table of Contents

Part 1: Guide

Chapter 1: Essentials LAPACK; Problems that LAPACK can Solve;
Computers for which LAPACK is Suitable; LAPACK Compared with LINPACK
and EISPACK; LAPACK and the BLAS; Documentation for LAPACK;
Availability of LAPACK; Installation of LAPACK; Support for LAPACK;
Known Problems in LAPACK; Other Related Software;

Chapter 2: Contents of LAPACK Structure of LAPACK; Driver Routines; Computational

Chapter 3: Performance of LAPACK Factors that Affect
Performance; The BLAS as the Key to Portability; Block Algorithms and
their Derivation; Examples of Block Algorithms in LAPACK; LAPACK

Chapter 4: Accuracy and Stability Sources of Error in
Numerical Calculations; How to Measure Errors; Further Details: How
Error Bounds are Derived; Error Bounds for Linear Equation Solving;
Error Bounds for Linear Least Squares Problems; Error Bounds for
Generalized Least Squares Problems; Error Bounds for the Symmetric
Eigenproblem; Error Bounds for the Nonsymmetric Eigenproblem; Error
Bounds for the Singular Value Decomposition; Error Bounds for the
Generalized Symmetric Definite Eigenproblem; Error Bounds for the
Generalized Nonsymmetric Eigenproblem; Error Bounds for the
Generalized Singular Value Decomposition; Error Bounds for Fast Level

Chapter 5: Documentation and Software Conventions Design and
Documentation of Argument Lists; Determining the Block Size for Block
Algorithms; Matrix Storage Schemes; Representation of Orthogonal or
Unitary Matrices;

Chapter 6: Installing LAPACK Routines Points to
Note; Installing ILAENV;

Chapter 7: Troubleshooting Common Errors in
Calling LAPACK Routines; Failures in LAPACK Routines; Wrong Results;
Poor Performance;

Appendix A: Index of Driver and Computational

Appendix B: Index of Auxiliary Routines;

Appendix C: Quick
Reference Guide to the BLAS;

Appendix D: Converting from LINPACK or

Appendix E: LAPACK Working Notes;

Part 2: Specifications of Routines Bibliography; Index by Keyword; Index by Routine Name

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