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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
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<H1><A NAME="SECTION03000000000000000000">
Guide</A>
</H1>
<P>
<BR><HR>
<!--Table of Child-Links-->
<A NAME="CHILD_LINKS"></A>
<UL>
<LI><A NAME="tex2html3992"
HREF="node6.html">Essentials</A>
<UL>
<LI><A NAME="tex2html3993"
HREF="node7.html">LAPACK</A>
<LI><A NAME="tex2html3994"
HREF="node8.html">Problems that LAPACK can Solve</A>
<LI><A NAME="tex2html3995"
HREF="node9.html">Computers for which LAPACK is Suitable</A>
<LI><A NAME="tex2html3996"
HREF="node10.html">LAPACK Compared with LINPACK and EISPACK</A>
<LI><A NAME="tex2html3997"
HREF="node11.html">LAPACK and the BLAS</A>
<LI><A NAME="tex2html3998"
HREF="node12.html">Availability of LAPACK</A>
<LI><A NAME="tex2html3999"
HREF="node13.html">Commercial Use of LAPACK</A>
<LI><A NAME="tex2html4000"
HREF="node14.html">Installation of LAPACK</A>
<LI><A NAME="tex2html4001"
HREF="node15.html">Documentation for LAPACK</A>
<LI><A NAME="tex2html4002"
HREF="node16.html">Support for LAPACK</A>
<LI><A NAME="tex2html4003"
HREF="node17.html">Errata in LAPACK</A>
<LI><A NAME="tex2html4004"
HREF="node18.html">Other Related Software</A>
</UL>
<LI><A NAME="tex2html4005"
HREF="node19.html">Contents of LAPACK</A>
<UL>
<LI><A NAME="tex2html4006"
HREF="node20.html">What's new in version 3.0?</A>
<LI><A NAME="tex2html4007"
HREF="node21.html">Structure of LAPACK</A>
<UL>
<LI><A NAME="tex2html4008"
HREF="node22.html">Levels of Routines</A>
<LI><A NAME="tex2html4009"
HREF="node23.html">Data Types and Precision</A>
<LI><A NAME="tex2html4010"
HREF="node24.html">Naming Scheme</A>
</UL>
<LI><A NAME="tex2html4011"
HREF="node25.html">Driver Routines</A>
<UL>
<LI><A NAME="tex2html4012"
HREF="node26.html">Linear Equations</A>
<LI><A NAME="tex2html4013"
HREF="node27.html">Linear Least Squares (LLS) Problems</A>
<LI><A NAME="tex2html4014"
HREF="node28.html">Generalized Linear Least Squares (LSE and GLM) Problems</A>
<LI><A NAME="tex2html4015"
HREF="node29.html">Standard Eigenvalue and Singular Value Problems</A>
<UL>
<LI><A NAME="tex2html4016"
HREF="node30.html">Symmetric Eigenproblems (SEP)</A>
<LI><A NAME="tex2html4017"
HREF="node31.html">Nonsymmetric Eigenproblems (NEP)</A>
<LI><A NAME="tex2html4018"
HREF="node32.html">Singular Value Decomposition (SVD)</A>
</UL>
<LI><A NAME="tex2html4019"
HREF="node33.html">Generalized Eigenvalue and Singular Value
Problems</A>
<UL>
<LI><A NAME="tex2html4020"
HREF="node34.html">Generalized Symmetric Definite Eigenproblems (GSEP)</A>
<LI><A NAME="tex2html4021"
HREF="node35.html">Generalized Nonsymmetric Eigenproblems (GNEP)</A>
<LI><A NAME="tex2html4022"
HREF="node36.html">Generalized Singular Value Decomposition (GSVD)</A>
</UL>
</UL>
<LI><A NAME="tex2html4023"
HREF="node37.html">Computational Routines</A>
<UL>
<LI><A NAME="tex2html4024"
HREF="node38.html">Linear Equations</A>
<LI><A NAME="tex2html4025"
HREF="node39.html">Orthogonal Factorizations and Linear Least Squares Problems</A>
<UL>
<LI><A NAME="tex2html4026"
HREF="node40.html"><I>QR</I> Factorization</A>
<LI><A NAME="tex2html4027"
HREF="node41.html"><B><I>LQ</I></B> Factorization</A>
<LI><A NAME="tex2html4028"
HREF="node42.html"><B><I>QR</I></B> Factorization with Column Pivoting</A>
<LI><A NAME="tex2html4029"
HREF="node43.html">Complete Orthogonal Factorization</A>
<LI><A NAME="tex2html4030"
HREF="node44.html">Other Factorizations</A>
</UL>
<LI><A NAME="tex2html4031"
HREF="node45.html">Generalized Orthogonal Factorizations and Linear Least Squares Problems</A>
<UL>
<LI><A NAME="tex2html4032"
HREF="node46.html">Generalized <B><I>QR</I></B> Factorization</A>
<LI><A NAME="tex2html4033"
HREF="node47.html">Generalized <B><I>RQ</I></B> Factorization</A>
</UL>
<LI><A NAME="tex2html4034"
HREF="node48.html">Symmetric Eigenproblems</A>
<LI><A NAME="tex2html4035"
HREF="node49.html">Nonsymmetric Eigenproblems</A>
<UL>
<LI><A NAME="tex2html4036"
HREF="node50.html">Eigenvalues, Eigenvectors and Schur Factorization</A>
<LI><A NAME="tex2html4037"
HREF="node51.html">Balancing</A>
<LI><A NAME="tex2html4038"
HREF="node52.html">Invariant Subspaces and Condition Numbers</A>
</UL>
<LI><A NAME="tex2html4039"
HREF="node53.html">Singular Value Decomposition</A>
<LI><A NAME="tex2html4040"
HREF="node54.html">Generalized Symmetric Definite Eigenproblems</A>
<LI><A NAME="tex2html4041"
HREF="node55.html">Generalized Nonsymmetric Eigenproblems</A>
<UL>
<LI><A NAME="tex2html4042"
HREF="node56.html">Eigenvalues, Eigenvectors and Generalized Schur Decomposition</A>
<LI><A NAME="tex2html4043"
HREF="node57.html">Balancing</A>
<LI><A NAME="tex2html4044"
HREF="node58.html">Deflating Subspaces and Condition Numbers</A>
</UL>
<LI><A NAME="tex2html4045"
HREF="node59.html">Generalized (or Quotient) Singular Value Decomposition</A>
</UL>
</UL>
<LI><A NAME="tex2html4046"
HREF="node60.html">Performance of LAPACK</A>
<UL>
<LI><A NAME="tex2html4047"
HREF="node61.html">Factors that Affect Performance</A>
<UL>
<LI><A NAME="tex2html4048"
HREF="node62.html">Vectorization</A>
<LI><A NAME="tex2html4049"
HREF="node63.html">Data Movement</A>
<LI><A NAME="tex2html4050"
HREF="node64.html">Parallelism</A>
</UL>
<LI><A NAME="tex2html4051"
HREF="node65.html">The BLAS as the Key to Portability</A>
<LI><A NAME="tex2html4052"
HREF="node66.html">Block Algorithms and their
Derivation</A>
<LI><A NAME="tex2html4053"
HREF="node67.html">Examples of Block Algorithms in LAPACK</A>
<UL>
<LI><A NAME="tex2html4054"
HREF="node68.html">Factorizations for Solving Linear Equations</A>
<LI><A NAME="tex2html4055"
HREF="node69.html"><B><I>QR</I></B> Factorization</A>
<LI><A NAME="tex2html4056"
HREF="node70.html">Eigenvalue Problems</A>
</UL>
<LI><A NAME="tex2html4057"
HREF="node71.html">LAPACK Benchmark</A>
</UL>
<LI><A NAME="tex2html4058"
HREF="node72.html">Accuracy and Stability</A>
<UL>
<LI><A NAME="tex2html4059"
HREF="node73.html">Sources of Error in Numerical Calculations</A>
<UL>
<LI><A NAME="tex2html4060"
HREF="node74.html">Further Details: Floating Point Arithmetic</A>
</UL>
<LI><A NAME="tex2html4061"
HREF="node75.html">How to Measure Errors</A>
<UL>
<LI><A NAME="tex2html4062"
HREF="node76.html">Further Details: How to Measure Errors</A>
</UL>
<LI><A NAME="tex2html4063"
HREF="node77.html">Further Details: How Error Bounds Are Derived</A>
<UL>
<LI><A NAME="tex2html4064"
HREF="node78.html">Standard Error Analysis</A>
<LI><A NAME="tex2html4065"
HREF="node79.html">Improved Error Bounds</A>
</UL>
<LI><A NAME="tex2html4066"
HREF="node80.html">Error Bounds for Linear Equation Solving</A>
<UL>
<LI><A NAME="tex2html4067"
HREF="node81.html">Further Details: Error Bounds for Linear Equation Solving</A>
</UL>
<LI><A NAME="tex2html4068"
HREF="node82.html">Error Bounds for Linear Least Squares Problems</A>
<UL>
<LI><A NAME="tex2html4069"
HREF="node83.html">Further Details: Error Bounds for Linear Least Squares
Problems</A>
</UL>
<LI><A NAME="tex2html4070"
HREF="node84.html">Error Bounds for Generalized Least Squares Problems</A>
<UL>
<LI><A NAME="tex2html4071"
HREF="node85.html">Linear Equality Constrained Least Squares Problem</A>
<UL>
<LI><A NAME="tex2html4072"
HREF="node86.html">Further Details:
Error Bounds for Linear Equality Constrained Least Squares Problems</A>
</UL>
<LI><A NAME="tex2html4073"
HREF="node87.html">General Linear Model Problem</A>
<UL>
<LI><A NAME="tex2html4074"
HREF="node88.html">Further Details: Error Bounds for General Linear Model Problems</A>
</UL>
</UL>
<LI><A NAME="tex2html4075"
HREF="node89.html">Error Bounds for the Symmetric Eigenproblem </A>
<UL>
<LI><A NAME="tex2html4076"
HREF="node90.html">Further Details: Error Bounds for the Symmetric Eigenproblem </A>
</UL>
<LI><A NAME="tex2html4077"
HREF="node91.html">Error Bounds for the Nonsymmetric Eigenproblem </A>
<UL>
<LI><A NAME="tex2html4078"
HREF="node92.html">Further Details: Error Bounds for the Nonsymmetric Eigenproblem</A>
<UL>
<LI><A NAME="tex2html4079"
HREF="node93.html">Overview</A>
<LI><A NAME="tex2html4080"
HREF="node94.html">Balancing and Conditioning</A>
<LI><A NAME="tex2html4081"
HREF="node95.html">Computing <B><I>s</I></B> and <IMG
WIDTH="29" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img2.png"
ALT="${\rm sep}$"></A>
</UL>
</UL>
<LI><A NAME="tex2html4082"
HREF="node96.html">Error Bounds for the Singular Value Decomposition</A>
<UL>
<LI><A NAME="tex2html4083"
HREF="node97.html">Further Details: Error Bounds for the Singular Value Decomposition</A>
</UL>
<LI><A NAME="tex2html4084"
HREF="node98.html">Error Bounds for the Generalized Symmetric Definite
Eigenproblem</A>
<UL>
<LI><A NAME="tex2html4085"
HREF="node99.html">Further Details: Error Bounds for the Generalized Symmetric Definite
Eigenproblem</A>
</UL>
<LI><A NAME="tex2html4086"
HREF="node100.html">Error Bounds for the Generalized Nonsymmetric Eigenproblem</A>
<UL>
<LI><A NAME="tex2html4087"
HREF="node101.html">Further Details: Error Bounds for the Generalized
Nonsymmetric Eigenproblem</A>
<UL>
<LI><A NAME="tex2html4088"
HREF="node102.html">Overview</A>
<LI><A NAME="tex2html4089"
HREF="node103.html">Balancing and Conditioning</A>
<LI><A NAME="tex2html4090"
HREF="node104.html">Computing <B><I>s</I><SUB><I>i</I></SUB></B>, <IMG
WIDTH="19" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img4.png"
ALT="$l_{\cal I}$">,
<IMG
WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
SRC="img5.png"
ALT="$r_{\cal I}$">
and
<IMG
WIDTH="38" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img6.png"
ALT="${\rm Dif}_u$">,
<IMG
WIDTH="34" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img7.png"
ALT="${\rm Dif}_l$"></A>
<LI><A NAME="tex2html4091"
HREF="node105.html">Singular Eigenproblems</A>
</UL>
</UL>
<LI><A NAME="tex2html4092"
HREF="node106.html">Error Bounds for the Generalized Singular Value Decomposition</A>
<UL>
<LI><A NAME="tex2html4093"
HREF="node107.html">Further Details: Error Bounds for the Generalized Singular Value Decomposition</A>
</UL>
<LI><A NAME="tex2html4094"
HREF="node108.html">Error Bounds for Fast Level 3 BLAS</A>
</UL>
<LI><A NAME="tex2html4095"
HREF="node109.html">Documentation and Software Conventions</A>
<UL>
<LI><A NAME="tex2html4096"
HREF="node110.html">Design and Documentation of Argument Lists</A>
<UL>
<LI><A NAME="tex2html4097"
HREF="node111.html">Structure of the Documentation</A>
<LI><A NAME="tex2html4098"
HREF="node112.html">Order of Arguments</A>
<LI><A NAME="tex2html4099"
HREF="node113.html">Argument Descriptions</A>
<LI><A NAME="tex2html4100"
HREF="node114.html">Option Arguments</A>
<LI><A NAME="tex2html4101"
HREF="node115.html">Problem Dimensions</A>
<LI><A NAME="tex2html4102"
HREF="node116.html">Array Arguments</A>
<LI><A NAME="tex2html4103"
HREF="node117.html">Work Arrays</A>
<LI><A NAME="tex2html4104"
HREF="node118.html">LWORK Query</A>
<LI><A NAME="tex2html4105"
HREF="node119.html">Error Handling and the Diagnostic Argument INFO</A>
</UL>
<LI><A NAME="tex2html4106"
HREF="node120.html">Determining the Block Size for Block Algorithms</A>
<LI><A NAME="tex2html4107"
HREF="node121.html">Matrix Storage Schemes</A>
<UL>
<LI><A NAME="tex2html4108"
HREF="node122.html">Conventional Storage</A>
<LI><A NAME="tex2html4109"
HREF="node123.html">Packed Storage</A>
<LI><A NAME="tex2html4110"
HREF="node124.html">Band Storage</A>
<LI><A NAME="tex2html4111"
HREF="node125.html">Tridiagonal and Bidiagonal Matrices</A>
<LI><A NAME="tex2html4112"
HREF="node126.html">Unit Triangular Matrices</A>
<LI><A NAME="tex2html4113"
HREF="node127.html">Real Diagonal Elements of Complex Matrices</A>
</UL>
<LI><A NAME="tex2html4114"
HREF="node128.html">Representation of Orthogonal or Unitary Matrices</A>
</UL>
<LI><A NAME="tex2html4115"
HREF="node129.html">Installing LAPACK Routines</A>
<UL>
<LI><A NAME="tex2html4116"
HREF="node130.html">Points to Note</A>
<LI><A NAME="tex2html4117"
HREF="node131.html">Installing ILAENV</A>
</UL>
<LI><A NAME="tex2html4118"
HREF="node132.html">Troubleshooting</A>
<UL>
<LI><A NAME="tex2html4119"
HREF="node133.html">Bug Report Checklist</A>
<LI><A NAME="tex2html4120"
HREF="node134.html">Installation Debugging Hints</A>
<LI><A NAME="tex2html4121"
HREF="node135.html">Common Errors in Calling LAPACK Routines</A>
<LI><A NAME="tex2html4122"
HREF="node136.html">Failures Detected by LAPACK Routines</A>
<UL>
<LI><A NAME="tex2html4123"
HREF="node137.html">Invalid Arguments and XERBLA</A>
<LI><A NAME="tex2html4124"
HREF="node138.html">Computational Failures and INFO <B>></B> 0</A>
</UL>
<LI><A NAME="tex2html4125"
HREF="node139.html">Wrong Results</A>
<LI><A NAME="tex2html4126"
HREF="node140.html">Poor Performance</A>
</UL>
<LI><A NAME="tex2html4127"
HREF="node141.html">Index of Driver and Computational Routines</A>
<UL>
<LI><A NAME="tex2html4128"
HREF="node142.html">Notes</A>
</UL>
<LI><A NAME="tex2html4129"
HREF="node143.html">Index of Auxiliary Routines</A>
<UL>
<LI><A NAME="tex2html4130"
HREF="node144.html">Notes</A>
</UL>
<LI><A NAME="tex2html4131"
HREF="node145.html">Quick Reference
Guide to the BLAS</A>
<LI><A NAME="tex2html4132"
HREF="node146.html">Converting from LINPACK or EISPACK</A>
<UL>
<LI><A NAME="tex2html4133"
HREF="node147.html">Notes</A>
</UL>
<LI><A NAME="tex2html4134"
HREF="node148.html">LAPACK Working Notes</A>
</UL>
<!--End of Table of Child-Links-->
<BR><HR>
<ADDRESS>
<I>Susan Blackford</I>
<BR><I>1999-10-01</I>
</ADDRESS>
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