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# LAPACK Users' Guide
Third Edition

UPDATED: 22 Aug 1999

- E. Anderson,
- Z. Bai,
- C. Bischof,
- S. Blackford,
- J. Demmel,
- J. Dongarra,
- J. Du Croz,
- A. Greenbaum,
- S. Hammarling,
- A. McKenney,
- D. Sorensen

  1999 by the Society for Industrial and Applied Mathematics. Certain derivative work portions have been copyrighted by the Numerical Algorithms Group Ltd.

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  Dedication

  This work is dedicated to Jim Wilkinson whose ideas and spirit have given us inspiration and influenced the project at every turn.

  Authors' Affiliations:
  E. Anderson
  University of Tennessee, Knoxville
  Z. Bai
  University of Kentucky and
  University of California, Davis
  C. Bischof
  Institute of Scientific Computing, Technical University Aachen, Germany
  L. S. Blackford (formerly L. S. Ostrouchov)
  University of Tennessee, Knoxville
  J. Demmel
  University of California, Berkeley
  J. Dongarra
  University of Tennessee, Knoxville and
  Oak Ridge National Laboratory
  J. Du Croz
  Numerical Algorithms Group Ltd. (retired)
  A. Greenbaum
  University of Washington
  S. Hammarling
  Numerical Algorithms Group Ltd.
  A. McKenney
  D. Sorensen
  Rice University

  - Contents
  - List of Tables
    - Preface to the Third Edition
    - Preface to the Second Edition
  - Guide
    - Essentials
      - LAPACK
      - Problems that LAPACK can Solve
      - Computers for which LAPACK is Suitable
      - LAPACK Compared with LINPACK and EISPACK
      - LAPACK and the BLAS
      - Availability of LAPACK
      - Commercial Use of LAPACK
      - Installation of LAPACK
      - Documentation for LAPACK
      - Support for LAPACK
      - Errata in LAPACK
      - Other Related Software
    - Contents of LAPACK
      - What's new in version 3.0?
      - Structure of LAPACK
        - Levels of Routines
        - Data Types and Precision
        - Naming Scheme
      - Driver Routines
        - Linear Equations
        - Linear Least Squares (LLS) Problems
        - Generalized Linear Least Squares (LSE and GLM) Problems
        - Standard Eigenvalue and Singular Value Problems
        - Generalized Eigenvalue and Singular Value Problems
      - Computational Routines
        - Linear Equations
        - Orthogonal Factorizations and Linear Least Squares Problems
        - Generalized Orthogonal Factorizations and Linear Least Squares Problems
        - Symmetric Eigenproblems
        - Nonsymmetric Eigenproblems
        - Singular Value Decomposition
        - Generalized Symmetric Definite Eigenproblems
        - Generalized Nonsymmetric Eigenproblems
        - Generalized (or Quotient) Singular Value Decomposition
    - Performance of LAPACK
      - Factors that Affect Performance
        - Vectorization
        - Data Movement
        - Parallelism
      - The BLAS as the Key to Portability
      - Block Algorithms and their Derivation
      - Examples of Block Algorithms in LAPACK
        - Factorizations for Solving Linear Equations
        - QR Factorization
        - Eigenvalue Problems
      - LAPACK Benchmark
    - Accuracy and Stability
      - Sources of Error in Numerical Calculations
        - Further Details: Floating Point Arithmetic
      - How to Measure Errors
        - Further Details: How to Measure Errors
      - Further Details: How Error Bounds Are Derived
        - Standard Error Analysis
        - Improved Error Bounds
      - Error Bounds for Linear Equation Solving
        - Further Details: Error Bounds for Linear Equation Solving
      - Error Bounds for Linear Least Squares Problems
        - Further Details: Error Bounds for Linear Least Squares Problems
      - Error Bounds for Generalized Least Squares Problems
        - Linear Equality Constrained Least Squares Problem
        - General Linear Model Problem
      - Error Bounds for the Symmetric Eigenproblem
        - Further Details: Error Bounds for the Symmetric Eigenproblem
      - Error Bounds for the Nonsymmetric Eigenproblem
        - Further Details: Error Bounds for the Nonsymmetric Eigenproblem
      - Error Bounds for the Singular Value Decomposition
        - Further Details: Error Bounds for the Singular Value Decomposition
      - Error Bounds for the Generalized Symmetric Definite Eigenproblem
        - Further Details: Error Bounds for the Generalized Symmetric Definite Eigenproblem
      - Error Bounds for the Generalized Nonsymmetric Eigenproblem
        - Further Details: Error Bounds for the Generalized Nonsymmetric Eigenproblem
      - Error Bounds for the Generalized Singular Value Decomposition
        - Further Details: Error Bounds for the Generalized Singular Value Decomposition
      - Error Bounds for Fast Level 3 BLAS
    - Documentation and Software Conventions
      - Design and Documentation of Argument Lists
        - Structure of the Documentation
        - Order of Arguments
        - Argument Descriptions
        - Option Arguments
        - Problem Dimensions
        - Array Arguments
        - Work Arrays
        - LWORK Query
        - Error Handling and the Diagnostic Argument INFO
      - Determining the Block Size for Block Algorithms
      - Matrix Storage Schemes
        - Conventional Storage
        - Packed Storage
        - Band Storage
        - Tridiagonal and Bidiagonal Matrices
        - Unit Triangular Matrices
        - Real Diagonal Elements of Complex Matrices
      - Representation of Orthogonal or Unitary Matrices
    - Installing LAPACK Routines
      - Points to Note
      - Installing ILAENV
    - Troubleshooting
      - Bug Report Checklist
      - Installation Debugging Hints
      - Common Errors in Calling LAPACK Routines
      - Failures Detected by LAPACK Routines
        - Invalid Arguments and XERBLA
        - Computational Failures and INFO > 0
      - Wrong Results
      - Poor Performance
    - Index of Driver and Computational Routines
      - Notes
    - Index of Auxiliary Routines
      - Notes
    - Quick Reference Guide to the BLAS
    - Converting from LINPACK or EISPACK
      - Notes
    - LAPACK Working Notes
  - Specifications of Routines
    - Notes
  - Bibliography
  - Index by Keyword
  - About this document ...

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