LAPACK Working Notes

Block Reduction of Matrices to Condensed Forms for Eigenvalue Computations
ANL, MCS-TM-99, September 1987.
J. Dongarra, S. Hammarling, and D. Sorensen

Computing Small Singular Values of Bidiagonal Matrices with Guaranteed High Relative Accuracy
ANL, MCS-TM-110, February 1988.
J. Demmel and W. Kahan

Guidelines for the Design of Symmetric Eigenroutines, SVD, and Iterative Refinement and Condition Estimation for Linear Systems
ANL, MCS-TM-111, March 1988.
J. Demmel, J. Du Croz, S. Hammarling, and D. Sorensen

Provisional Contents
ANL, MCS-TM-38, September 1988.
C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, and D. Sorensen

Tools to Aid in the Analysis of Memory Access Patterns for FORTRAN Programs
ANL, MCS-TM-120, June 1988.
O. Brewer, J. Dongarra, and D. Sorensen

Computing Accurate Eigensystems of Scaled Diagonally Dominant Matrices
ANL, MCS-TM-126, December 1988.
J. Barlow and J. Demmel

On a Block Implementation of Hessenberg Multishift QR Iteration
ANL, MCS-TM-127, January 1989.
Z. Bai and J. Demmel

A Test Matrix Generation Suite
ANL, MCS-P69-0389, March 1989.
J. Demmel and A. McKenney

Installing and Testing the Initial Release of LAPACK -- Unix and Non-Unix Versions
ANL, MCS-TM-130, May 1989.
E. Anderson and J. Dongarra

The Bidiagonal Singular Value Decomposition and Hamiltonian Mechanics
ANL, MCS-TM-133, August 1989.
P. Deift, J. Demmel, L.-C. Li, and C. Tomei

On the Conditioning of the Nonsymmetric Eigenproblem: Theory and Software
UT, CS-89-86, October 1989.
Z. Bai, J. Demmel, and A. McKenney

On Floating Point Errors in Cholesky
UT, CS-89-87, October 1989.
J. Demmel

Jacobi's Method is More Accurate than QR
UT, CS-89-88, October 1989.
J. Demmel and K. Veselic

Results from the Initial Release of LAPACK
UT, CS-89-89, November 1989.
E. Anderson and J. Dongarra

Experiments with QR/QL Methods for the Symmetric Tridiagonal Eigenproblem
UT, CS-89-92, November 1989.
A. Greenbaum and J. Dongarra

Implementation Guide for LAPACK
UT, CS-90-101, April 1990.
E. Anderson and J. Dongarra

Evaluating Block Algorithm Variants in LAPACK
UT, CS-90-103, April 1990.
E. Anderson and J. Dongarra

LAPACK: A Portable Linear Algebra Library for High-Performance Computers
UT, CS-90-105, May 1990.
E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. DuCroz, A. Greenbaum, S. Hammarling, A. McKenney, D. Sorensen

Stability of Block Algorithms with Fast Level 3 BLAS
UT, CS-90-110, July 1990.
J. Demmel and N. Higham

Improved Error Bounds for Underdetermined System Solvers
UT, CS-90-113, August 1990.
J. Demmel and N. Higham

LAPACK Block Factorization Algorithms on the Intel iPSC/860
UT, CS-90-115, October, 1990.
J. Dongarra and S. Ostrouchov

Numerical Considerations in Computing Invariant Subspaces
UT, CS-90-117, October, 1990.
J. Dongarra, S. Hammarling, and J. Wilkinson

Prospectus for an Extension to LAPACK: A Portable Linear Algebra Library for High-Performance Computers
UT, CS-90-118, November 1990.
E. Anderson, C. Bischof, J. Demmel, J. Dongarra, J. DuCroz, S. Hammarling, and W. Kahan

Stability of Methods for Matrix Inversion
UT, CS-90-119, October, 1990.
J. DuCroz, N. Higham

The IBM RISC System/6000 and Linear Algebra Operations
UT, CS-90-122, December 1990.
J. Dongarra, P. Mayes, G. Radicati

On Global Combine Operations
UT, CS-91-129, April 1991.
R. van de Geijn

Reduction to Condensed Form for the Eigenvalue Problem on Distributed Memory Architectures
UT, CS-91-130, April 1991.
J. Dongarra, R. van de Geijn

Generalized QR Factorization and its Applications
UT, CS-91-131, April 1991.
E. Anderson, Z. Bai, J. Dongarra

Generalized Incremental Condition Estimation
UT, CS-91-132, May 1991.
C. Bischof, P.T.P. Tang

Robust Incremental Condition Estimation
UT, CS-91-133, May 1991.
C. Bischof, P.T.P. Tang

Workshop on the BLACS
UT, CS-91-134, May 1991.
J. J. Dongarra

Implementation guide for LAPACK
UT, CS-91-138, August 1991.
E. Anderson, J. Dongarra, and S. Ostrouchov

Robust Triangular solvers
UT, CS-91-142, August, 1991.
E. Anderson

Two Dimensional Basic Linear Algebra Communication Subprograms
UT, CS-91-138, October, 1991.
Jack J. Dongarra and Robert A. van de Geijn

On a Direct Algorithm for Computing Invariant Subspaces with Specified Eigenvalues
UT, CS-91-139, November, 1991.
Z. Bai and J. Demmel

On Designing Portable High Performance Numerical Libraries
UT, CS-91-141, July, 1991.
James Demmel, Jack Dongarra, and W. Kahan

Block LU Factorization
UT, CS-92-149, February 1992.
James Demmel, Nick Higham, Rob Schreiber

Installation Guide for LAPACK
UT, CS-92-151, March, 1992.
Updated: October, 1994 (VERSION 2.0)
Edward Anderson, Jack Dongarra, and Susan Ostrouchov

Perturbation Theory and Backward Error for $AX-XB=C$
UT, CS-92-153, April, 1992.
Nick Higham

A Look at Scalable Dense Linear Algebra Libraries
UT, CS-92-155, April, 1992.
Jack Dongarra, Robert van de Geijn and David Walker

Performance of LAPACK: A Portable Library of Numerical Linear Algebra Routines
UT, CS-92-156, May 1992.
Edward Anderson and Jack Dongarra

The Inherent Inaccuracy of Implicit Tridiagonal QR
UT, CS-92-162, May 1992.
J. Demmel

Computing the Generalized Singular Value Decomposition
UT, CS-92-163, May 1992.
Z. Bai and J. Demmel

Open Problems in Numerical Linear Algebra
UT, CS-92-164, May 1992.
J. Demmel

On Computing Accurate Singular Values and Eigenvalues of Matrices with Acyclic Graphs
UT, CS-92-166, May 1992.
J. Demmel and W. Gragg

A Specification for Floating Point Parallel Prefix
UT, CS-92-167, May 1992.
J. Demmel

Distributed Sparse Data Structures for Linear Algebra Operations
UT, CS-92-169, May 1992.
Victor Eijkhout

Qualitative Properties of the Conjugate Gradient and Lanczos Methods in a Matrix Framework
UT, CS-92-170, May 1992.
Victor Eijkhout

A Cartesian Parallel Nested Dissection Algorithm
UT, CS-92-178, June 1992.
Michael T. Heath and Padma Raghavan

Trading Off Parallelism and Numerical Stability
UT, CS-92-179, June 1992.
J.W. Demmel

On Swapping Diagonal Blocks in Real Schur Form
UT, CS-92-182, October 1992.
Z. Bai and J.W. Demmel

ScaLAPACK: A Scalable Linear Algebra for Distributed Memory Concurrent Computers
UT, CS-92-181, November 1992.
J. Choi, J. Dongarra, R. Pozo, and D. Walker

Reducing Communication Costs in the Conjugate Gradient Algorithm on Distributed Memory Multiprocessors
UT, CS-93-185, January 1993.
E.F. D'Azevedo, V.L. Eijkhout and C.H. Romine

PUMMA: Parallel Universal Matrix Multiplication Algorithms on Distributed Memory Concurrent Computers
UT, CS-93-187, May 1993.
Jaeyoung Choi, Jack J. Dongarra, and David W. Walker

The Design of Linear Algebra Libraries for High Performance Computer
UT, CS-93-188, June 1993.
Jack Dongarra and David Walker

Faster Numerical Algorithms via Exception Handling
UT, CS-93-192, March 1993.
James W. Demmel and Xiaoye Li

Parallel Numerical Linear Algebra
UT, CS-93-192, March 1993.
James W. Demmel, Michael T. Heath, and Henk A. van der Vorst

An Object Oriented Design for High Performance Linear Algebra on Distributed Memory Architectures
UT, CS-93-200, August 1993.
J. Dongarra, R. Pozo, and D. Walker

Distributed Solution of Sparse Linear Systems
UT, CS-93-201, August 1993.
Michael T. Heath and Padma Raghavan

Line and Plane Separators
UT, CS-93-202, August 1993.
Michael T. Heath and Padma Raghavan

Distributed Sparse Gaussian Elimination and Orthogonal Factorization
UT, CS-93-203, August 1993.
Padma Raghavan

Parallel Matrix Transpose Algorithms on Distributed Memory Concurrent Computers
UT, CS-93-215, November, 1993.
Jaeyoung Choi, Jack J. Dongarra, and David W. Walker

A Characterization of Polynomial Iterative Methods
UT, CS-93-216, November 1993.
Victor Eijkhout

Performance Complexity of $LU$ Factorization with Efficient Pipelining and Overlap on a Multiprocessor
UT, CS-93-218, December, 1993.
F. Desprez, J. Dongarra, and B. Tourancheau

A Highly Parallel Algorithm for the Reduction of a Nonsymmetric Matrix to Block Upper-Hessenberg Form
UT, CS-94-221, February 1994.
Michael W. Berry, Jack J. Dongarra and Youngbae Kim

A Serial Implementation of Cuppen's Divide and Conquer Algorithm for the Symmetric Eigenvalue Problem
UT, CS-94-225, March 1994.
J. Rutter

On the Correctness of Parallel Bisection in Floating Point
UT, CS-94-228, March 1994.
James Demmel, Inderjit Dhillon, and Huan Ren

IBM RS/6000-550 & -590 Performance for Selected Routines in ESSL
UT, CS-94-231, April 1994.
Jack Dongarra and Michael Kolatis

The Computation of Elementary Unitary Matrices
UT, CS-94-233, October 1995.
R. Lehoucq

Basic Linear Algebra Communication Subprograms: Analysis and Implementation Across Multiple Parallel Architectures
UT, CS-94-234, May 1994.
R. Clint Whaley

A Sparse Matrix Library in C++ for High Performance Architectures
UT, CS-94-236, July 1994.
J. Dongarra, A. Lumsdaine, X. Niu, R. Pozo, and K. Remington

LAPACK-Style Algorithms and Software for Solving the Generalized Sylvester Equation and Estimaing the Separating Between Regular Matrix Pairs
UT, CS-94-237, July 1994.
Bo Kagstrom and Peter Poromaa

Algorithic Bombardment for the Iterative Solution of Linear Systems: A Poly-Iterative Approach
UT, CS-94-239, August, 1994.
Richard Barrett, Michael Berry, Jack Dongarra, Victor Eijkhout, and Charles Romine

Basic Concepts for Distributed Sparse Linear Algebra Operations
UT, CS-94-240, August, 1994.
Victor Eijkhout and Roldan Pozo

Computational variants of the CGS and BiCGstab methods
UT, CS-94-241, August, 1994.
Victor Eijkhout

Parallelizing the QR Algorithm for the Unsymmetric Algebraic Eigenvalue Problem: Myths and Reality
UT, CS-94-244, August, 1994.
Greg Henry and Robert van de Geijn

The Design and Implementation of the ScaLAPACK LU, QR, and Cholesky Factorization Routines
UT, CS-94-246, September, 1994.
J. Choi, J. J. Dongarra, S. Ostrouchov, A. P. Petitet, D. W. Walker, and R. C. Whaley

Quick Installation Guide for LAPACK on Unix Systems
UT, CS-94-249, September, 1994.
J. Dongarra and S. Ostrouchov

Call Conversion Interface (CCI) for LAPACK/ESSL
UT, CS-94-250, August, 1994.
J. Dongarra and M. Kolatis

Relative Perturbation Bounds for the Unitary Polar Factor
UT, CS-94-251, September, 1994.
Ren-Cang Li

Relative Perturbation Theory: (I) Eigenvalue Variations
UT, CS-94-252, September, 1994.
Ren-Cang Li

Relative Perturbation Theory: (II) Eigenspace Variations
UT, CS-94-253, September, 1994.
Ren-Cang Li

The Performance of Finding Eigenvalues and Eigenvectors of Dense Symmetric Matrices on Distributed Memory Computers
UT, CS-94-254, September, 1994.
J. Demmel and K. Stanley

Computing Eigenspaces with Specified Eigenvalues of a Regular Matrix Pair (A,B) and Condition Estimation: Theory, Algorithms and Software
UT, CS-94-255, September, 1994.
B. Kagstrom and P. Poromaa

Efficient Computation of the Singular Value Decomposition with Applications to Least Squares Problems
UT, CS-94-257, October, 1994.
Ming Gu, James Demmel, and Inderjit Dhillon

Solving Secular Equations Stably and Efficiently
UT, CS-94-260, November, 1994.
Ren-Cang Li

Algorithm-Based Diskless Checkpointing for Fault Tolerant Matrix Operations
UT, CS-94-268, December 1994.
J. S. Plank, Y. Kim, and J. J. Dongarra

The Spectral Decomposition of Nonsymmetric Matrices on Distributed Memory Computers
UT, CS-95-273, January 1995.
Z. Bai, J. Demmel, J. Dongarra, A. Petitet, H. Robinson, and K. Stanley

The Design of a Parallel Dense Linear Algebra Software Library: Reduction to Hessenberg, Tridiagonal, and Bidiagonal Form
UT, CS-95-275, February 1995.
J. Choi, J. Dongarra, and D. Walker

Installation Guide for ScaLAPACK
UT, CS-95-280, March, 1995.
UPDATED: November 17, 1996 (VERSION 1.4).
J. Choi, J. Demmel, I. Dhillon, J. Dongarra, S. Ostrouchov, A. Petitet, K. Stanley, D. Walker, and R. C. Whaley

A User's Guide to the BLACS v1.0
UT, CS-95-281, March 1995.
J. Dongarra and R. C. Whaley

ScaLAPACK: A Portable Linear Algebra Library for Distributed Memory Computers - Design Issues and Performance
UT, CS-95-283, March 1995.
J. Choi, J. Demmel, I. Dhillon, J. Dongarra, S. Ostrouchov, A. Petitet, K. Stanley, D. Walker, and R. C. Whaley

SUMMA: Scalable Universal Matrix Multiplication Algorithm
UT, CS-95-286, April 1995.
R. A. van de Geijn and J. Watts

Modeling the Benefits of Mixed Data and Task Parallelism
UT, CS-95-289, May 1995.
S. Chakrabarti, J. Demmel, and D. Yelick

LAPACK++ V. 1.0: High Performance Linear Algebra Users' Guide
UT, CS-95-290, May 1995.
J. Dongarra, R. Pozo, and D. Walker

Reverse Communication Interface for Linear Algebra Templates for Iterative Methods
UT, CS-95-291, May 1995.
J. Dongarra, V. Eijkhout, and A. Kalhan

A Proposal for a Set of Parallel Basic Linear Algebra Subprograms
UT, CS-95-292, May 1995.
J. Choi, J. Dongarra, S. Ostrouchov, A. Petitet, D. Walker, and R. C. Whaley

A Proposal for a Fortran 90 Interface for LAPACK
UT, CS-95-295, July 1995.
J. J. Dongarra, J. Du Croz, S. Hammarling, J. Wasniewski, and A. Zemla

IML++ v. 1.2: Iterative Methods Library Reference Guide
UT, CS-95-303, August 1995.
J. Dongarra, A. Lumsdaine, R. Pozo, and K. Remington

A Supernodal Approach to Sparse Partial Pivoting
UT, CS-95-304, September 1995.
J. W. Demmel, S. C. Eisenstat, J. R. Gilbert, X. S. Li, and J. W. H. Liu

Iterative Refinement and LAPACK
UT, CS-95-308, October 1995.
N. J. Higham

Stability of the Diagonal Pivoting Method with Partial Pivoting
UT, CS-95-309, October 1995.
N. J. Higham

Templates for Linear Algebra Problems
UT, CS-95-311, October 1995.
Z. Bai, D. Day, J. Demmel, J. Dongarra, M. Gu, A. Ruhe, and H. van der Vorst

GEMM-Based Level 3 BLAS: High-Performance Model Implementations and Performance Evaluation Benchmark
UT, CS-95-315, November 1995.
B. Kagstrom, P. Ling, and C. Van Loan

GEMM-Based Level 3 BLAS: Installation, Tuning and Use of the Model Implementations and the Performance Evaluation Benchmark
UT, CS-95-316, November 1995.
B. Kagstrom, P. Ling, and C. Van Loan

BLAS Technical Workshop
UT, CS-95-317, November 1995.
J. Dongarra, S. Hammarling, and S. Ostrouchov

Key Concepts For Parallel Out-Of-Core LU Factorization
UT, CS-96-324, April 1996.
J. J. Dongarra, S. Hammarling, and D. W. Walker

Optimizing Matrix Multiply using PHiPAC: a Portable, High-Performance, ANSI C Coding Methodology
UT, CS-96-326, May 1996.
J. Bilmes, K. Asanovic, J. Demmel, D. Lam, and C.-W. Chin

Practical Experience in the Dangers of Heterogeneous Computing
UT, CS-96-330, July 1996.
L. S. Blackford, A. Cleary, J. Demmel, I. Dhillon, J. Dongarra, S. Hammarling, A. Petitet, H. Ren, K. Stanley, and R. C. Whaley

Block-Partitioned Algorithms for Solving the Linear Least Squares Problem
UT, CS-96-333, July 1996.
G. Quintana-Orti, E. S. Quintana-Orti, and A. Petitet

A BLAS-3 Version of the QR Factorization with Column Pivoting
UT, CS-96-334, August 1996.
G. Quintana-Orti, X. Sun, and C. Bischof

On the Error Analysis and Implementation of Some Eigenvalue Decomposition and Singular Value Decomposition Algorithms
UT, CS-96-336, September 1996.
H. Ren

Parallel Matrix Distributions: Have we been doing it all right?
UT, CS-96-340, November 1996.
M. Sidani and B. Harrod

A Fortran 90 Interface for LAPACK
UT, CS-96-341, December 1996.
L. Susan Blackford, Jack J. Dongarra, Jeremy Du Croz, Sven Hammarling, Jerzy Wasniewski

The Design and Implementation of the Parallel Out-of-core ScaLAPACK LU, QR, and Cholesky Factorization Routines
UT, CS-97-347, January 1997.
J. J. Dongarra and E. F. D'Azevedo

Computing the Singular Value Decomposition with High Relative Accuracy
UT, CS-97-348, February 1997.
J. Demmel, M. Gu, S. Eisenstat, I. Slapnicar, K. Veselic, and Z. Drmac

Scheduling Block-Cyclic Array Redistribution
UT, CS-97-349, February 1997.
F. Desprez, J. Dongarra, A. Petitet, C. Randriamaro, and Y. Robert

A Parallel Implementation of the Nonsymmetric QR Algorithm for Distributed Memory Architectures
UT, CS-97-352, March 1997.
G. Henry, D. Watkins, and J. Dongarra

A New Deflation Criterion for the QR Algorithm
UT, CS-97-353, March 1997.
M. Ahues and F. Tisseur

A Test Matrix Collection for Non-Hermitian Eigenvalue Problems
UT, CS-97-355, March 1997.
Z. Bai, D. Day, J. Demmel and J. Dongarra

An Asynchronous Parallel Supernodal Algorithm for Sparse Gaussian Elimination
UT, CS-97-357, April 1997.
J. Demmel, J. Gilbert, and X. Li

Implementation in ScaLAPACK of Divide-and-Conquer Algorithms for Banded and Tridiagonal Linear Systems
UT, CS-97-358, April 1997.
A. Cleary and J. Dongarra

Performance Improvements to LAPACK for the Cray Scientific Library
UT, CS-97-359, April 1997.
E. Anderson and M. Fahey