LAPACK Working Notes

Most of these working notes are available from netlib, where they can only be obtained in postscript form. To receive a list of available postscript reports, send email to netlib@ornl.gov of the form: send index from lapack/lawns

1.

J. W. DEMMEL, J. J. DONGARRA, J. DU CROZ, A. GREENBAUM, S. HAMMARLING, AND D. SORENSEN, Prospectus for the Development of a Linear Algebra Library for High-Performance Computers, ANL, MCS-TM-97, September 1987.

2.

J. J. DONGARRA, S. HAMMARLING, AND D. SORENSEN, Block Reduction of Matrices to Condensed Forms for Eigenvalue Computations, ANL, MCS-TM-99, September 1987.

3.

J. W. DEMMEL AND W. KAHAN, Computing Small Singular Values of Bidiagonal Matrices with Guaranteed High Relative Accuracy, ANL, MCS-TM-110, February 1988.

4.

J. W. DEMMEL, J. DU CROZ, S. HAMMARLING, AND D. SORENSEN, Guidelines for the Design of Symmetric Eigenroutines, SVD, and Iterative Refinement and Condition Estimation for Linear Systems, ANL, MCS-TM-111, March 1988.

5.

C. BISCHOF, J. W. DEMMEL, J. J. DONGARRA, J. DU CROZ, A. GREENBAUM, S. HAMMARLING, AND D. SORENSEN, Provisional Contents, ANL, MCS-TM-38, September 1988.

6.

O. BREWER, J. J. DONGARRA, AND D. SORENSEN, Tools to Aid in the Analysis of Memory Access Patterns for FORTRAN Programs, ANL, MCS-TM-120, June 1988.

7.

J. BARLOW AND J. W. DEMMEL, Computing Accurate Eigensystems of Scaled Diagonally Dominant Matrices, ANL, MCS-TM-126, December 1988.

8.

Z. BAI AND J. W. DEMMEL, On a Block Implementation of Hessenberg Multishift QR Iteration, ANL, MCS-TM-127, January 1989.

9.

J. W. DEMMEL AND A. MCKENNEY, A Test Matrix Generation Suite, ANL, MCS-P69-0389, March 1989.

10.

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

11.

P. DEIFT, J. W. DEMMEL, L.-C. LI, AND C. TOMEI, The Bidiagonal Singular Value Decomposition and Hamiltonian Mechanics, ANL, MCS-TM-133, August 1989.

12.

P. MAYES AND G. RADICATI, Banded Cholesky Factorization Using Level 3 BLAS, ANL, MCS-TM-134, August 1989.

13.

Z. BAI, J. W. DEMMEL, AND A. MCKENNEY, On the Conditioning of the Nonsymmetric Eigenproblem: Theory and Software, UT, CS-89-86, October 1989.

14.

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

15.

J. W. DEMMEL AND K. VESELIC, Jacobi's Method is More Accurate than QR, UT, CS-89-88, October 1989.

16.

E. ANDERSON AND J. J. DONGARRA, Results from the Initial Release of LAPACK, UT, CS-89-89, November 1989.

17.

A. GREENBAUM AND J. J. DONGARRA, Experiments with QR/QL Methods for the Symmetric Tridiagonal Eigenproblem, UT, CS-89-92, November 1989.

18.

E. ANDERSON AND J. J. DONGARRA, Implementation Guide for LAPACK, UT, CS-90-101, April 1990.

19.

E. ANDERSON AND J. J. DONGARRA, Evaluating Block Algorithm Variants in LAPACK, UT, CS-90-103, April 1990.

20.

E. ANDERSON, Z. BAI, C. BISCHOF, J. W. DEMMEL, J. J. DONGARRA, J. DU CROZ, A. GREENBAUM, S. HAMMARLING, A. MCKENNEY, AND D. SORENSEN, LAPACK: A Portable Linear Algebra Library for High-Performance Computers, UT, CS-90-105, May 1990.

21.

J. DU CROZ, P. MAYES, AND G. RADICATI, Factorizations of Band Matrices Using Level 3 BLAS, UT, CS-90-109, July 1990.

22.

J. W. DEMMEL AND N. J. HIGHAM, Stability of Block Algorithms with Fast Level 3 BLAS, UT, CS-90-110, July 1990.

23.

J. W. DEMMEL AND N. J. HIGHAM, Improved Error Bounds for Underdetermined System Solvers, UT, CS-90-113, August 1990.

24.

J. J. DONGARRA AND S. OSTROUCHOV, LAPACK Block Factorization Algorithms on the Intel iPSC/860, UT, CS-90-115, October, 1990.

25.

J. J. DONGARRA, S. HAMMARLING, AND J. H. WILKINSON, Numerical Considerations in Computing Invariant Subspaces, UT, CS-90-117, October, 1990.

26.

E. ANDERSON, C. BISCHOF, J. W. DEMMEL, J. J. DONGARRA, J. DU CROZ, S. HAMMARLING, AND W. KAHAN, Prospectus for an Extension to LAPACK: A Portable Linear Algebra Library for High-Performance Computers, UT, CS-90-118, November 1990.

27.

J. DU CROZ AND N. J. HIGHAM, Stability of Methods for Matrix Inversion, UT, CS-90-119, October, 1990.

28.

J. J. DONGARRA, P. MAYES, AND G. RADICATI, The IBM RISC System/6000 and Linear Algebra Operations, UT, CS-90-122, December 1990.

29.

R. VAN DE GEIJN, On Global Combine Operations, UT, CS-91-129, April 1991.

30.

J. J. DONGARRA AND R. VAN DE GEIJN, Reduction to Condensed Form for the Eigenvalue Problem on Distributed Memory Architectures, UT, CS-91-130, April 1991.

31.

E. ANDERSON, Z. BAI, AND J. J. DONGARRA, Generalized QR Factorization and its Applications, UT, CS-91-131, April 1991.

32.

C. BISCHOF AND P. TANG, Generalized Incremental Condition Estimation, UT, CS-91-132, May 1991.

33.

C. BISCHOF AND P. TANG, Robust Incremental Condition Estimation, UT, CS-91-133, May 1991.

34.

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

35.

E. ANDERSON, J. J. DONGARRA, AND S. OSTROUCHOV, Implementation guide for LAPACK, UT, CS-91-138, August 1991. (replaced by Working Note 41)

36.

E. ANDERSON, Robust Triangular Solves for Use in Condition Estimation, UT, CS-91-142, August 1991.

37.

J. J. DONGARRA AND R. VAN DE GEIJN, Two Dimensional Basic Linear Algebra Communication Subprograms, UT, CS-91-138, October 1991.

38.

Z. BAI AND J. W. DEMMEL, On a Direct Algorithm for Computing Invariant Subspaces with Specified Eigenvalues, UT, CS-91-139, November 1991.

39.

J. W. DEMMEL, J. J. DONGARRA, AND W. KAHAN, On Designing Portable High Performance Numerical Libraries, UT, CS-91-141, July 1991.

40.

J. W. DEMMEL, N. J. HIGHAM, AND R. SCHREIBER, Block LU Factorization, UT, CS-92-149, February 1992.

41.

E. ANDERSON, J. J. DONGARRA, AND S. OSTROUCHOV, Installation Guide for LAPACK, UT, CS-92-151, February 1992.

42.

N. J. HIGHAM, Perturbation Theory and Backward Error for AX-XB=C., UT, CS-92-153, April, 1992.

43.

J. J. DONGARRA, R. VAN DE GEIJN, AND D. W. WALKER, A Look at Scalable Dense Linear Algebra Libraries, UT, CS-92-155, April, 1992.

44.

E. ANDERSON AND J. J. DONGARRA, Performance of LAPACK: A Portable Library of Numerical Linear Algebra Routines, UT, CS-92-156, May 1992.

45.

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

46.

Z. BAI AND J. W. DEMMEL, Computing the Generalized Singular Value Decomposition, UT, CS-92-163, May 1992.

47.

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

48.

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

49.

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

50.

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

51.

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

52.

M. T. HEATH AND P. RAGHAVAN, A Cartesian Parallel Nested Dissection Algorithm, UT, CS-92-178, June 1992.

53.

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

54.

Z. BAI AND J. W. DEMMEL, On Swapping Diagonal Blocks in Real Schur Form, UT, CS-92-182, October 1992.

55.

J. CHOI, J. J. DONGARRA, R. POZO, AND D. W. WALKER, ScaLAPACK: A Scalable Linear Algebra for Distributed Memory Concurrent Computers, UT, CS-92-181, November 1992.

56.

E. F. D'AZEVEDO, V. L. EIJKHOUT AND C. H. ROMINE, Reducing Communication Costs in the Conjugate Gradient Algorithm on Distributed Memory Multiprocessors, UT, CS-93-185, January 1993.

57.

J. CHOI, J. J. DONGARRA, AND D. W. WALKER, PUMMA: Parallel Universal Matrix Multiplication Algorithms on Distributed Memory Concurrent Computers, UT, CS-93-187, May 1993.

58.

J. J. DONGARRA AND D. W. WALKER, The Design of Linear Algebra Libraries for High Performance Computer, UT, CS-93-188, June 1993.

59.

J. W. DEMMEL AND X. LI, Faster Numerical Algorithms via Exception Handling, UT, CS-93-192, March 1993.

60.

J. W. DEMMEL, M. T. HEATH, AND H. A. VAN DER VORST, Parallel Numerical Linear Algebra, UT, CS-93-192, March 1993.

61.

J. J. DONGARRA, R. POZO, AND D. W. WALKER, An Object Oriented Design for High Performance Linear Algebra on Distributed Memory Architectures, UT, CS-93-200, August 1993.

62.

M. T. HEATH AND P. RAGHAVAN, Distributed Solution of Sparse Linear Systems, UT, CS-93-201, August 1993.

63.

M. T. HEATH AND P. RAGHAVAN, Line and Plane Separators, UT, CS-93-202, August 1993.

64.

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

65.

J. CHOI, J. J. DONGARRA, AND D. W. WALKER, Parallel Matrix Transpose Algorithms on Distributed Memory Concurrent Computers, UT, CS-93-215, November, 1993.

66.

V. L. EIJKHOUT, A Characterization of Polynomial Iterative Methods, UT, CS-93-216, November, 1993.

67.

F. DESPREZ, J. DONGARRA, AND B. TOURANCHEAU, Performance Complexity of Factorization with Efficient Pipelining and Overlap on a Multiprocessor, UT, CS-93-218, December, 1993.

68.

MICHAEL W. BERRY, JACK J. DONGARRA AND YOUNGBAE KIM, A Highly Parallel Algorithm for the Reduction of a Nonsymmetric Matrix to Block Upper-Hessenberg Form, UT, CS-94-221, January, 1994.

69.

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

70.

J. W. DEMMEL, INDERJIT DHILLON, AND HUAN REN, On the Correctness of Parallel Bisection in Floating Point, UT, CS-94-228, April, 1994.

71.

J. DONGARRA AND M. KOLATIS, IBM RS/6000-550 & -590 Performance for Selected Routines in ESSL, UT, CS-94-231, April, 1994.

72.

R. LEHOUCQ, The Computation of Elementary Unitary Matrices, UT, CS-94-233, May, 1994.

73.

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

74.

J. DONGARRA, A. LUMSDAINE, X. NIU, R. POZO, AND K. REMINGTON, A Sparse Matrix Library in C++ for High Performance Architectures, UT, CS-94-236, July, 1994.

75.

B. KÅGSTRÖM AND P. POROMAA, Computing Eigenspaces with Specified Eigenvalues of a Regular Matrix Pair (A,B) and Condition Estimation: Theory, Algorithms and Software, UT, CS-94-237, July, 1994.

76.

R. BARRETT, M. BERRY, J. DONGARRA, V. EIJKHOUT, AND C. ROMINE, Algorithic Bombardment for the Iterative Solution of Linear Systems: A Poly-Iterative Approach, UT, CS-94-239, August, 1994.

77.

V. EIJKHOUT AND R. POZO, Basic Concepts for Distributed Sparse Linear Algebra Operations, UT, CS-94-240, August, 1994.

78.

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

79.

G. HENRY AND R. VAN DE GEIJN, Parallelizing the QR Algorithm for the Unsymmetric Algebraic Eigenvalue Problem: Myths and Reality, UT, CS-94-244, August, 1994.

80.

J. CHOI, J. J. DONGARRA, S. OSTROUCHOV, A. P. PETITET, D. W. WALKER, AND R. C. WHALEY, The Design and Implementation of the ScaLAPACK LU, QR, and Cholesky Factorization Routines, UT, CS-94-246, September, 1994.

81.

J. J. DONGARRA AND S. OSTROUCHOV, Quick Installation Guide for LAPACK on Unix Systems, UT, CS-94-249, September, 1994.

82.

J. J. DONGARRA AND M. KOLATIS, Call Conversion Interface (CCI) for LAPACK/ESSL, UT, CS-94-250, August, 1994.

83.

R. C. LI, Relative Perturbation Bounds for the Unitary Polar Factor, UT, CS-94-251, September, 1994.

84.

R. C. LI, Relative Perturbation Theory: (I) Eigenvalue Variations, UT, CS-94-252, September, 1994.

85.

R. C. LI, Relative Perturbation Theory: (II) Eigenspace Variations, UT, CS-94-253, September, 1994.

86.

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

87.

B. KÅGSTRÖM AND P. POROMAA, 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.