Contents

• List of Tables
  • Preface to the Second Edition
  • Preface to the First 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
    • Documentation for LAPACK
    • Availability of LAPACK
    • Installation of LAPACK
    • Support for LAPACK
    • Known Problems in LAPACK
    • Other Related Software
      • LAPACK++
      • CLAPACK
      • ScaLAPACK
      • LAPACK routines exploiting IEEE arithmetic
  • Contents of LAPACK
    • 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
        • Symmetric Eigenproblems (SEP)
        • Nonsymmetric Eigenproblems (NEP)
        • Singular Value Decomposition (SVD)
      • Generalized Eigenvalue and Singular Value Problems
        • Generalized Symmetric Definite Eigenproblems (GSEP)
        • Generalized Nonsymmetric Eigenproblems (GNEP)
        • Generalized Singular Value Decomposition (GSVD)
    • Computational Routines
      • Linear Equations
      • Orthogonal Factorizations and Linear Least Squares Problems
        • QR Factorization
        • LQ Factorization
        • QR Factorization with Column Pivoting
        • Complete Orthogonal Factorization
        • Other Factorizations
      • Generalized Orthogonal Factorizations and Linear Least Squares Problems
        • Generalized QR Factorization
        • Generalized RQ factorization
      • Symmetric Eigenproblems
      • Nonsymmetric Eigenproblems
        • Eigenvalues, Eigenvectors and Schur Factorization
        • Balancing
        • Invariant Subspaces and Condition Numbers
      • 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
    • 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
        • Overview
        • Balancing and Conditioning
        • Computing s and sep
    • 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
    • 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
      • 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
    • 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
• References
• Index
• About this document ...