Footnotes
LAPACK Users' Guide Release 2.0
Contents
 LAPACK Compared with LINPACK and EISPACK
 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
 LAPACK and the BLAS
 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
 Documentation for LAPACK
 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
 Availability of LAPACK
 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
 Installation of LAPACK
  About this document ... 
 Support for LAPACK
 Known Problems in LAPACK
 Other Related Software
 LAPACK++
 CLAPACK
List of Tables
 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
 Preface to the Second Edition
 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
 Preface to the First Edition
 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
 Guide
 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
 Essentials
 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
 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
 Problems that LAPACK can Solve
 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
 Computers for which LAPACK is Suitable
 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
Contents
Contents
LAPACK Users' Guide Release 2.0
 Band Storage
 Tridiagonal and Bidiagonal Matrices
 Generalized   factorization