101. Matran: A Matrix Wrapper For Fortran 95 Fortran 95 wrapper that implements matrix operations and computes matrix decompositions using Lapack and the Blas. http://www.cs.umd.edu/~stewart/matran/Matran.html

MATRAN A MATRIX WRAPPER FOR FORTRAN 95 G. W. Stewart Department of Computer Science Institute for Advanced Computer Studies University of Maryland Mathematical and Computations Sciences Division NIST stewart@cs.umd.edu http://www.cs.umd.edu/~stewart/ Contents Introduction Current Status Obtaining and using Matran Change Log ... Acknowledgements Introduction (top) Matran (pronounced MAY-tran) is a Fortran 95 wrapper that implements matrix operations and computes matrix decompositions using Lapack and the Blas. Although Matran is not based on a formally defined matrix language, it provides the flavor and convenience of coding in matrix oriented systems like Matlab, Octave, etc. By using routines from Lapack and the Blas, Matran allows the user to obtain the computational benefits of these packages with minimal fuss and bother. Detailed information about Matran may be found in the Matran Writeup ( ps pdf ). Here we give a general overview of Matran, its organization, and its capabilities. Organization Matran consists of a number of Fortran 95 modules, which fall into five categories.

102. Automatically Tuned Linear Algebra Software (ATLAS) The ATLAS (Automatically Tuned Linear Algebra Software) project is an ongoing research effort focusing on applying empirical techniques in order to provide http://math-atlas.sourceforge.net/

Automatically Tuned Linear Algebra Software (ATLAS) [Home] [Docs] [FAQ] [Errata] ... [SourceForge Summary Page] The ATLAS (Automatically Tuned Linear Algebra Software) project is an ongoing research effort focusing on applying empirical techniques in order to provide portable performance. At present, it provides C and Fortran77 interfaces to a portably efficient BLAS implementation, as well as a few routines from LAPACK If you download the software, it is critically important that you check the ATLAS errata file . This file lists all known errors in ATLAS, and all known system problems (eg., compiler errors, etc), and any fixes and workarounds. See the faq for support help. The newest ATLAS papers can be found here [Home] [Docs] [FAQ] ... [Timings]

103. Expokit - Matrix Exponential Software Package For Dense And Sparse Matrices Software package for computing small dense and large sparse matrix exponentials in Fortran and Matlab. Usable in C/C++. http://www.maths.uq.edu.au/expokit/

Download Changes Paper (PDF) Download Support Expokit is a software package that provides matrix exponential routines for small dense or very large sparse matrices, real or complex. Here you will find the source code in Fortran and Matlab . The native Fortran version is embeddable in C/C++ Understanding Expokit w(t) = exp(tA)v is the analytic solution of the homogeneous ODE problem: w'(t) = Aw(t), w(0) = v. w(t) = exp(tA)v + t*phi(tA)u, where phi(x) = (exp(x)-1)/x, is the analytic solution of the nonhomogeneous ODE problem: w'(t) = Aw(t) + u, w(0) = v. Expokit handles both cases. Frequently Asked Questions From Computing Reviews: This amazingly complete paper gives the theoretical background of the methods, presents applications, provides computational results for a standard set of pathological matrices, and closes with a mini-user's manual (...) It is entirely self-contained (...) Here we are given several sure ways to compute (...) exponentials, and these with rather sharp error bounds. Full Review Moler and Van Loan: The most extensive software for computing the matrix exponential that we are aware of is Expokit.

104. LUMOD: Updating A Dense Square Factorization L*C = U Updates a dense square factorization L*C = U, when rows and columns of C are added, deleted or replaced. http://www.stanford.edu/group/SOL/software/lumod.html

Home Software Personnel Students, Alumni, Visitors ... Systems Using SOL Publications Books Dissertations Journal Papers Classics ... Dantzig Memoriam In association with SCCM iCME Memorial Fellowships Dantzig-Lieberman Fund Gene Golub Fund Systems Optimization Laboratory Stanford University Huang Engineering Center Stanford, CA 94305-4121 USA LUMOD: Updating a dense square factorization L*C = U AUTHOR: M. A. Saunders CONTENTS: Fortran software for updating a dense square factorization L*C = U when rows and columns of C are added, deleted or replaced. (Suitable as basis package for dense simplex method, or for updating sparse factorizations via the Schur-complement method.) L is square, stored by rows in a 1-D array. It is a product of stabilized elementary transformations. U is upper triangular, stored by rows in a 1-D array. The dimension of C, L and U may change. If maxn is the largest C allowed for, the total storage is maxn^2 for L and maxn(maxn+1)/2 for U. REFERENCES: Stabilized elementary transformations are described in J. H. Wilkinson, The Algebraic Eigenvalue Problem, Clarendon Press, Oxford (1965).

105. SIAM: Conference On Applied Linear Algebra (LA09) Presentation slides and some audio files available of talks from the special session on The History of Numerical Linear Algebra http://www.siam.org/meetings/la09/

CONFERENCES This conference is organized by the SIAM Activity Group on Linear Algebra (SIAG/LA) Report from the Forward Looking Session: Role of Linear Algebra in Industrial Applications Presentation slides and some audio files available of talks from the special session on The History of Numerical Linear Algebra Announcements The triennial SIAG/Linear Algebra Prize will be awarded at the meeting. As of January 12, 2009 , a valid ESTA approval is required for all Visa Waiver Program (VWP) to travel to the United States. Please visit http://travel.state.gov/visa/temp/without/without_1990.html for additional information and procedures. Organizing Committee Raymond Chan, Chinese University of Hong Kong, Hong Kong Inderjit Dhillon, University of Texas at Austin Mark Embree, Rice University Andreas Frommer, University of Wuppertal, Germany Anne Greenbaum, University of Washington Chen Greif, University of British Columbia, Canada Misha Kilmer, Tufts University Michael Mahoney, Stanford University James Nagy, Emory University

106. Parallel Algorithms Project Website Codes to solve linear systems with the GMRES and conjugate gradient methods, among other topics. http://www.cerfacs.fr/algor/Setup/JSEnabledFrameset.html

107. Linear Algebra : Mkaz.com Jun 30, 2005 Linear Algebra Calculator (JavaScript) A calculator that can solve a linear system of 3 equations and 3 unknowns, includes explanation http://mkaz.com/math/line_alg.html

108. LAPACK -- Linear Algebra PACKage Fortran 77 routines for solving systems of simultaneous linear equations, least-squares solutions of linear systems of equations, eigenvalue problems, and singular value problems. http://www.netlib.org/lapack/index.html

LAPACK Linear Algebra PACKage L A P A C K L -A P -A C -K L A P A -C -K L -A P -A -C K L A -P -A C K L -A -P A C -K ( l l l l ) ( a -a a -a ) 1/4 * ( p p -p -p ) ( a -a -a a ) ( c c -c -c ) ( k -k -k k ) Version 3.2.2 LAPACK User Forum lapack@cs.utk.edu Subscribe to the LAPACK announcement list # Accesses ... [LICENSE] LAPACK is written in Fortran90 and provides routines for solving systems of simultaneous linear equations, least-squares solutions of linear systems of equations, eigenvalue problems, and singular value problems. The associated matrix factorizations (LU, Cholesky, QR, SVD, Schur, generalized Schur) are also provided, as are related computations such as reordering of the Schur factorizations and estimating condition numbers. Dense and banded matrices are handled, but not general sparse matrices. In all areas, similar functionality is provided for real and complex matrices, in both single and double precision. If you're uncertain of the LAPACK routine name to address your application's needs, check out the

109. Matrix Analysis & Applied Linear Algebra By Carl D. Meyer. Full text in PDF with errata, updates and solutions. http://www.matrixanalysis.com/

110. Software Iterative Methods: GMRESR And BiCGstab(ell) Fortran 77 subroutines by Henk A. van der Vorst for the iterative methods GMRESR and BiCGstab(ell). These are methods for the iterative solution of large and typically sparse systems of linear equations with a nonsymmetric matrix. http://www.math.uu.nl/people/vorst/software.html

GMRESR and BiCGstab(ell) Here you may find Fortran77 subroutines for the iterative methods GMRESR and BiCGstab(ell). These are methods for the iterative solution of large and typically sparse systems of linear equations with a nonsymmetric matrix. The methods have been introduced in the following papers: H.A. Van der Vorst and C. Vuik GMRESR: a Family of Nested GMRES Methods , Numerical Linear Algebra with Applications, Vol.1(4), pp. 369-386, 1994. G.L.G. Sleijpen and D.R. Fokkema BiCGstab(ell) for Linear Equations involving Unsymmetric Matrices with Complex Spectrum ETNA , 1 (1993), pp. 11-32. If you are a user of the Bi-CGSTAB iterative method , please note that BiCGstab(ell=1) will give you the Bi-CGSTAB algorithm. Moreover, this implementation is the so-called "vanilla version" of Bi-CGSTAB/BiCGstab(ell), i.e. it includes two recent important enhancements for improvement of stability and robustness: G.L.G. Sleijpen and H.A. van der Vorst Reliable updated residuals in hybrid Bi-CG methods , Computing 56 (1996), pp. 141-163.

111. A Geometric Review Of Linear Algebra File Format PDF/Adobe Acrobat Quick View http://www.cns.nyu.edu/~eero/NOTES/geomLinAlg.pdf

112. Lapack Blas Fortran Windows Win32 Binaries Download Headers Header Files C C++ Binaries compiled with Intel Fortran 9.0, links to LAPACK source code, and make file to create binaries. By David Svoboda. http://www.fi.muni.cz/~xsvobod2/misc/lapack/

Go back to my homepage The source codes of lapack and blas packages are available from http://www.netlib.org/liblist.html . Since no open source Fortran compiler is natively available for Win32 platform, the precompiled binaries of these two packages can be downloaded from http://www.netlib.org/lapack/archives/ as well. Unfortunately, there are some bugs in those lib files. When building any C++ application in MSVC .NET against lapack.lib and blas.lib you can reveal several linking troubles. For this purpose appropriate makefiles in source codes were changed and corresponding binary files were built using Intel Fortran compiler (ver 11.0): shared version (statically-linked, release): download shared version (dynamically-loaded, release): download shared version (statically-linked, debug): download shared version (dynamically-loaded, debug): download static version (no more available) notes: when linking your application against blas*.lib and lapack*.lib you'll be asked to provide the following files: ifconsol.lib, libifcoremt.lib, libifport.lib, libmmt.lib, libirc.lib, svml_disp.lib . *) For this reason I recommend to use shared version. You'll avoid troubles with distribution of several mandatory files. 30 day evaluation version is available If you want to build the binaries on your own Download the original lapack source codes as well as a patched tar-gzipped lapack/blas directory structure lapack-3.2.1-win32-patch.tgz

113. Linear Algebra File Format Microsoft Powerpoint View as HTML http://www.ecse.rpi.edu/Homepages/shivkuma/teaching/sp2007/wbn2007/wbn2007-linea

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114. Lapack-ex The example programs illustrate the use of the double precision versions of the LAPACK drivers. http://www.nag.com/lapack-ex/lapack-ex.html

Numerical Algorithms Group Home Page Contact Us Request Info Site Map Next: Introduction Example Programs for the LAPACK Drivers These web pages contain example programs for the LAPACK driver routines (located on the Netlib Repository web site) Please read the Introduction first. Introduction Real Linear Equation Routines Complex Linear Equation Routines Real Linear Least Squares Routines ... Site Map � The Numerical Algorithms Group Trademarks

115. BILUM: Multi-Level Block ILU Preconditioning Techniques For Solving General Spar Code by Yousef Saad and Jun Zhang to solve general sparse linear systems by using Krylov subspace methods preconditioned by some multi-level block ILU (BILUM) preconditioning techniques. http://www.cs.uky.edu/~jzhang/bilum.html

BILUM A Software Package of Multi-Level Block ILU Preconditioning Techniques for Solving General Sparse Linear Systems Preliminary Examination Version, November 1997 Latest Update, March 18, 1998 Yousef Saad Department of Computer Science and Engineering University of Minneapolis Minneapolis, MN 55455, USA Jun Zhang Department of Computer Science University of Kentucky Lexington, KY 405060047, USA Introduction to BILUM The advantages of BILUM compared to other more traditional incomplete LU (ILU) factorizations are the followings: Robustness Experiments on a large number of test matrices arising in various domains including finite element methods, finite difference methods, computational fluid dynamics, high-order discretized convection-diffusion equations, Harwell-Boeing collections, FIDAP matrices, Simon matrices, Wigto matrices, driven cavity problems, have shown that BILUM is much more robust than traditional ILU-type preconditioners. For many hard problems, the improved robustness and faster convergence rate are accompanied by less memory consumption, which is a surprising contrary to many so-called robust preconditioning techniques. Scalability Grid-independent convergence is almost synonymous with multigrid methods. In fact, without some multi-level or multi-scale implementation, the convergence rate of an iterative method tends to decrease as the size of the problems increases. This is a very undesirable feature as iterative methods are usually designed to solve large scale problems. However, experiments on certain type of problems have shown that BILUM demonstrates nearly grid-independent convergence. For some convection-diffusion problems, its convergence rate can be shown to be nearly independent of the strength of the convection or the Reynolds number.

116. ITPACK Home Page Collection of Fortran 77 subroutines for solving large sparse linear systems by adaptive accelerated iterative algorithms. http://rene.ma.utexas.edu/CNA/ITPACK/

The ITPACK Software Package ITPACK, developed at the Center for Numerical Analysis , the University of Texas at Austin , is a collection of subroutines for solving large sparse linear systems by adaptive accelerated iterative algorithms. NSPCG (for NonSymmetric Preconditioned Conjugate Gradient) is a wide collection of subroutines for solving large sparse linear systems using iterative algorithms. with a selection of many more preconditioners, accelerators, and data formats. It contains all of the ITPACK subroutines. Please send email to Dr. David R. Kincaid if you have any questions about ITPACK. Download ITPACK 2C : Double-precision ITPACK 2C source code Testing Routine for double-precision ITPACK 2C ITPACK 2C : Single-precision ITPACK 2C source code Testing Routine for single-precision ITPACK 2C ITPACKV 2D : ITPACKV 2D source code (vectorized for Cray Y-MP) Testing Routine : for ITPACKV 2D ITPACK 2C User's Guide in LaTeX ITPACKV 2D User's Guide in LaTeX Online Manuals ITPACK 2C User's Guide ITPACKV 2D User's Guide Installation You should create a directory for the downloaded files. Note that you can compile your program using the following command:

117. MINRES: Sparse Symmetric Equations Solves sparse linear equations using a conjugate-gradient type method. http://www.stanford.edu/group/SOL/software/minres.html

Home Software Personnel Students, Alumni, Visitors ... Systems Using SOL Publications Books Dissertations Journal Papers Classics ... Dantzig Memoriam In association with SCCM iCME Memorial Fellowships Dantzig-Lieberman Fund Gene Golub Fund Systems Optimization Laboratory Stanford University Huang Engineering Center Stanford, CA 94305-4121 USA MINRES: Sparse Symmetric Equations AUTHORS: C. C. Paige M. A. Saunders CONTRIBUTORS: Sou-Cheng Choi CONTENTS: Implementation of a conjugate-gradient type method for solving sparse linear equations: Solve Ax = b or (A - sI)x = b MINRES is really solving one of the least-squares problems or If A is symmetric (and A - sI is nonsingular), SYMMLQ may be slightly more reliable. If A is unsymmetric, use LSQR REFERENCES: C. C. Paige and M. A. Saunders (1975). Solution of sparse indefinite systems of linear equations , SIAM J. Numerical Analysis 12, 617-629. S.-C. Choi (2006). Iterative Methods for Singular Linear Equations and Least-Squares Problems , PhD thesis, Stanford University. RELEASE: 22 Jul 2003: f77 files derived from f77 version of SYMMLQ. Preconditioning permitted; singular systems not.

118. Linear Algebra - CliffsNotes Get free articles in linear algebra and other math subjects when you need help with your algebra and math homework and tests, courtesy of CliffsNotes. http://www.cliffsnotes.com/study_guide/Linear-Algebra.topicArticleId-20807.html

CliffsNotes - The Fastest Way to Learn My Cart My Account Help Home ... Math Linear Algebra Linear Algebra Homework Help in Linear Algebra from CliffsNotes! Need homework and test-taking help in linear algebra? These articles can help you understand more advanced algebra topics. Click the plus sign to view articles in a section, or use the Search box below to find something specific. Search Linear Algebra Related Topics: Algebra I Algebra II Vector Algebra The Space R The Space R ... n Matrix Algebra Matrices Operations with Matrices Linear Systems Introduction to Linear Systems Solutions to Linear Systems Gaussian Elimination Using Elementary Row Operations to Determine ... A Real Euclidean Vector Spaces Subspaces of R n The Nullspace of a Matrix ... More Vector Spaces; Isomorphism The Determinant Definitions of the Determinant Laplace Expansions for the Determinant The Classical Adjoint of a Square Matrix Eigenvalues and Eigenvectors Eigenvalue and Eigenvector Defined Determining the Eigenvalues of a Matrix Determining the Eigenvectors of a Matrix Eigenspaces ... Trigonometry Glossary Ask Cliff [Please help] to solve this algebra (factoring) problem: x3 - 3x2 - x + 3 = 0 My teacher talks about the Greatest Common Factor. What's so great about it?

119. NIST Fortran Sparse BLAS: Toolkit Implementation Provides computational kernels for fundamental sparse matrix operations. http://math.nist.gov/~KRemington/fspblas/

The NIST Fortran Sparse BLAS (v. 0.5) Sparse Matrix Computational Kernels Karin Remington National Institute of Standards and Technology See the working document of the BLAST Sparse Subcommittee for related information. As part of the ongoing standardization effort in the BLAS Technical Forum , we are releasing the NIST Fortran Sparse BLAS Library for public review. OVERVIEW DOCUMENTATION AND RELATED PAPERS DISTRIBUTION BUG REPORTS OVERVIEW The original NIST Sparse BLAS implementation (in C) of the Toolkit interface provides an maintenance friendly approach to optimization of BLAS kernel routines via an automatic generation of special case routines. This approach provides high performance with little or no hand-tuning of source code. It does, however, result in a very large number of kernel routine interfaces; essentially one interface for each Toolkit level routine parameter combination. For those who find this to be undesirable, and not worth the performance and maintenance benefits, a straightforward Fortran implementation of the Toolkit routines is now available. These routines are NOT optimized for any particular parameter combinations, but can be optimized to suit the needs of a particular vendor/site.

120. Linear Algebra And Its Applications, Third Edition Update Welcome to the Companion Website for Linear Algebra and Its Applications, Third Edition Update. Linear Algebra and Its Applications, Third Edition Update http://wps.aw.com/aw_lay_linearalg_updated_3/

No Frames Version Welcome to the Companion Website for Linear Algebra and Its Applications, Third Edition Update. Site Introduction Site Navigation

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