#

**Complete list of publications: **
You can browse all our publications including
papers, working notes,
users' guides, and
recent presentations from this list.

**Papers Related to PRISM: **

Auslander, L. & A. Tsao "On parallelizable eigensolvers", Adv. Appl. Math., vol. 13, pp. 253-261, 1992 (preprint appeared as Technical Report SRC-TR-91-028, Supercomputing Research Center) as compressed postscript or postscript.

Lederman, S., A. Tsao, & T. Turnbull, "A parallelizable eigensolver for real diagonalizable matrices with real eigenvalues", Technical Report TR-91-042, Supercomputing Research Center (1991, 22 pages) as compressed postscript or postscript. (also see WN#20)

**PRISM Working Notes (WN):**

Bischof, C. & X. Sun, "A divide-and-conquer method for computing complementary invariant subspaces of symmetric matrices", Argonne National Lab Technical Report ANL-MCS-P286-0192 (March 1992, 13 pages, WN#1, obsolete)

Bai, Z., "Error analysis of the Lanczos algorithm for the nonsymmetric eigenvalue problem", appeared as Math. Comp., Vol.62, pp. 209-226, 1994 (April 1992, 21 pages, WN#2) as compressed postscript or postscript.

Bischof, C. & X. Sun, "A framework for symmetric band reduction and tridiagonalization", Argonne National Lab Preprint MCS P298-0392 (July 1992, 16 pages, WN#3) as compressed postscript or postscript.

Bai, Z., "Progress in the numerical solution of the nonsymmetric eigenvalue problem", appeared as Numer. Lin. Alg. Appl., Vol. 2(3), pp. 219-234, 1995 (Oct. 1992, 17 pages, WN#4) as compressed postscript or postscript.

Bai, Z. & J. Demmel,"Design of a Parallel Nonsymmetric Eigenroutine Toolbox (Part I)", Univ. of Kentucky Research report 92-09 (Dec. 1992, 30 pages, WN#5) as compressed postscript or postscript. A shorter version appeared in proceeding of the Sixth SIAM Conference on Parallel Processing for Scientific Computing in Norfork, VA, pp.391-398, SIAM, Philadelphia, 1993.

Tsao, A. & T. Turnbull, "A Comparison of Algorithms for Banded Matrix Multiplication", Technical Report SRC-TR-093-092, Supercomputing Research Center (1993, 9 pages, WN#6) as compressed postscript or postscript.

Huss-Lederman, S., E. Jacobson, A. Tsao, & G. Zhang, "Matrix Multiplication on the Intel Touchstone DELTA", appeared in proceedings of Sixth SIAM conference on Parallel Processing for Scientific Computing in Norfork, VA (March 1993, 9 pages, WN#7) as compressed postscript or postscript.

Bischof, C., M. Marques, & X. Sun, "Parallel bandreduction and tridiagonalization", appeared in proceedings of Sixth SIAM conference on Parallel Processing for Scientific Computing in Norfork, VA (March 1993, 8 pages, WN#8) as compressed postscript or postscript.

Huss-Lederman, S., A. Tsao, & G. Zhang, "A Parallel Implementation of the Invariant Subspace Decomposition Algorithm for Dense Symmetric Matrices", appeared in proceedings of Sixth SIAM conference on Parallel Processing for Scientific Computing in Norfork, VA (March 1993, 8 pages, WN#9) as compressed postscript or postscript.

Bischof, C., Huss-Lederman, S., E. Jacobson, X. Sun, & A. Tsao, "On the Impact of HPF Data Layout on the Design of Efficient and Maintainable Parallel Linear Algebra Libraries", a description of virtual 2D torus wrap, submitted as comments to the HPF working group (March 1993, 8 pages, WN#10) as compressed postscript or postscript.

Huss-Lederman, S., E. Jacobson, A. Tsao, & G. Zhang, "Matrix Multiplication on the Intel Touchstone DELTA", Technical Report SRC-TR-93-101, Supercomputing Research Center, (May 1993, 18 pages, WN#11). This is an expanded version of WN#7 and has been superseded by WN#14.

Bischof, C., S. Huss-Lederman, X. Sun, & A. Tsao,"The PRISM Project: Infrastructure and Algorithms for Parallel Eigensolvers", appeared in proceedings of the Scalable Parallel Libraries conference in Starksville, MS (October 1993, 9 pages, WN#12). as compressed postscript or postscript

Huss-Lederman, S., E. Jacobson, A. Tsao, "Comparison of Scalable Parallel Matrix Multiplication Libraries", appeared in proceedings of the Scalable Parallel Libraries conference in Starksville, MS (October 1993, 8 pages, WN#13) as compressed postscript or postscript.

Huss-Lederman, S., E. Jacobson, A. Tsao, & G. Zhang, "Matrix Multiplication on the Intel Touchstone DELTA", (revised), Appeared in Concurrency: Practice and Experience, Vol. 6 (7), Oct. 1994, pp. 571-594 (Feb. 1994, 21 pages, WN#14) as compressed postscript or postscript.

Bischof, C., S. Huss-Lederman, X. Sun, A. Tsao, T. Turnbull,"Parallel Performance of a Symmetric Eigensolver based on the Invariant Subspace Decomposition Approach", appeared in proceedings of Scalable High Performance Computing Conference 1994 (March 1994, 8 pages, WN#15) as compressed postscript or postscript.

Bischof, C., X. Sun, A. Tsao, & T. Turnbull, "A Study of the Invariant Subspace Decomposition Algorithm for Banded Symmetric Matrices", appeared in Proceedings of the 5th SIAM Conference on Applied Linear Algebra (March 1994, 6 pages, WN#16) as compressed postscript or postscript.

Bischof, C., B. Lang, & X. Sun, "Parallel Tridiagonalization through Two-Step Band Reduction", appeared in proceedings of Scalable High Performance Computing Conference 1994 (March 1994, 5 pages, WN#17) as compressed postscript or postscript.

Bai, Z., J. Demmel, & M. Gu, "Inverse Free Parallel Spectral Divide and Conquer Algorithms for Nonsymmetric Eigenproblems", Research Report 94-01, Department of Mathematics, University of Kentucky, appeared as Numer. Math., Vol.76, pp.279-308, 1997 (April 1994, 33 pages, WN#18) as compressed postscript or postscript.

Sun, X. & C. Bischof, "A Basis-Kernel Representation of Orthogonal Matrices", Argonne National Lab Preprint MCS-P431-0594 (1994, 20 pages, WN#19) as compressed postscript or postscript.

Huss-Lederman, S., A. Tsao, & T. Turnbull, "A parallelizable eigensolver for real diagonalizable matrices with real eigenvalues", appeared in SIAM J. Sci. Comput., vol. 18, pp. 869-885, 1997 (24 pages, WN#20) as compressed postscript or postscript.

Bischof, C. & X. Sun, "On orthogonal block elimination", Argonne Preprint MCS-P450-0794 (1994, 27 pages, WN#21) as compressed postscript or postscript.

Bischof, C., S. Huss-Lederman, X. Sun, A. Tsao, & T. Turnbull, "A case study of MPI: Portable and efficient libraries", appeared in Proceedings, Seventh SIAM Conference on Parallel Processing for Scientific Computing, San Francisco, (February 1995, 6 pages, WN#22) as compressed postscript or postscript.

Bischof, C., S. Huss-Lederman, X. Sun, A. Tsao, & T. Turnbull, "Parallel studies of the Invariant Subspace Decomposition Approach for banded symmetric matrices", appeared in Proceedings, Seventh SIAM Conference on Parallel Processing for Scientific Computing, San Francisco, (February 1995, 6 pages, WN#23) as compressed postscript or postscript.

Bischof, C. & X. Sun, "On the design of a tridiagonalization routine for banded matrices", appeared in Proceedings, Seventh SIAM Conference on Parallel Processing for Scientific Computing, San Francisco, (February 1995, 6 pages, WN#24) as compressed postscript or postscript.

Bischof, C. H. & X. Sun, "On tridiagonalizing and diagonalizing symmetric matrices with repeated eigenvalues", Argonne Preprint MCS-P545-1095. (1995, 21 pages, WN#25) as compressed postscript or postscript.

Quintana-orti, G., Sun, X., & Bischof, C. H., "A BLAS-3 version of the QR factorization with column pivoting", Argonne Preprint MCS-P551-1295.(1995, 9 pages, WN#26) as compressed postscript or postscript.

Sun, X., "On elementary unitary and -unitary transformations", Duke CS Preprint CS-1995-27. (November 1995, 15 pages, WN#27) as compressed postscript or postscript

Bai, Z. & J. Demmel, "Design of a Parallel Nonsymmetric Eigenroutine Toolbox (Part II)", Univ. of Kentucky Research report (Jan. 1996, 24 pages, WN#28) as compressed postscript or postscript. A shorter verion of this paper has been accepted for publication as, "Using the Matrix Sign Function to Compute Invariant Subspaces", SIAM. J. Mat. Anal. Appl.

Sun, X., "Aggregations of Elementary Transformations", Duke University report (March 1996, 16 pages, WN#29) as compressed postscript or postscript.

Bischof, C. & G. Quintana-orti, "Computing Rank-Revealing QR Factorizations for Dense Matrices", Argonne Preprint MCS-P559-0196. (1996, 24 pages, WN#30) as compressed postscript or postscript.

Bischof, C. & G. Quintana-orti, "Codes for Rank-Revealing QR Factorizations for Dense Matrices", Argonne Preprint MCS-P560-0196 (1996, 6 pages, WN#31) as compressed postscript or postscript.

Sun, X. & E. S. Quintana-orti, "Spectral Division Methods for Block Generalized Schur Decomposition", Duke CS Preprint CS_1996-13. Duke University. (1996, 19 pages, WN#32) as compressed postscript or postscript. Matlab files for the examples are also available.

Huss-Lederman, S., E. M. Jacobson, J. R. Johnson, A. Tsao, & T. Turnbull, "Implementation of Strassen's Algorithm for Matrix Multiplication." Proceedings of Supercomputing '96 (August 1996, 25 pages, WN#33) as compressed postscript or postscript.

Huss-Lederman, S., E. M. Jacobson, J. R. Johnson, A. Tsao, & T. Turnbull,"Strassen's Algorithm for Matrix Multiplication: Modeling, Analysis, and Implementation", Center for Computing Sciences. (1996, 67 pages, WN#34) as compressed postscript or postscript and the Errata page for WN34 as compressed postscript or postscript.

Wu, Y.-J. J., A. A. Alpatov, C. Bischof, & R. A. van de Geijn, "A Parallel Implementation of Symmetric Band Reduction Using PLAPACK", Proceedings of Scalable Parallel Library Conference, Mississippi Staate. (October 1996, 8 pages, WN#35) as compressed postscript or postscript.

Bischof, C., B. Lang, & X. Sun, "A Framework for Symmetric Band Reduction", Argonne Preprint MCS-P586-0496. (April 1996, 18 pages, wn#36) as compressed postscript or postscript.

Bischof, C., B. Lang, & X. Sun, "The SBR Toolbox - Software for Successive Band Reduction", Argonne Preprint MCS-P587-0496. (April 1996, 16 pages, WN#37) as compressed postscript or postscript.

Chtchelkanova, A., J. Gunnels, G. Morrow, J. Overfelt, & R. A. van de Geijn, "Parallel Implementation of BLAS: General Techniques for Level 3 BLAS", PLAPACK Working Note #4, TR-95-40, Department of Computer Sciences, University of Texas (October 1995, 30 pages, WN#38) as postscript. To appear in Concurrency: Practice and Experience.

Sun, X. & E.S. Quintana-Orti, "The Generalized Newton Iteration for the Matrix Sign Function", (August 1997, 15 pages, WN#39) as compressed postscript or postscript.

Quintana, E.S., G. Quintana, X. Sun & R. van de Geijn, "Efficient matrix inversion via Gauss-Jordan elimination and its parallelization", PLAPACK Working Note #8, TR-98-19, Department of Computer Sciences, University of Texas (August 1998, 18 pages, WN#40) as postscript.

Huss-Lederman, S., E.S. Quintana-Orti, X. Sun, & Y.-J. Y., "Parallel spectral division via the generalized matrix sign function", (March 1999, 14 pages, WN#41) as compressed postscript or postscript.

**PRISM Software UserGuide:**

SYISDA & BiMMeR: Contains the user and installation guide for Syisda and BiMMeR. This file is also included with each of the distribution files as compressed postscript or postscript.
DGEFMM: A portable Implementation of Strassen's Algorithm as compressed postscript or postscript.

**Selected Presentations:**

Wu, Y.-J. J., A. A. Alpatov, C. Bischof, & R. A. van de Geijn, "Parallel SBR: a PLAPACK based PRISM kernel", Eighth SIAM Conference on Parallel Processing for Scientific Computing, March 1997 as compressed postscript or postscript.

Bischof, C., W. George, S. Huss-Lederman, X. Sun, A. Tsao, T. Turnbull, and Y.-J. J. Wu, "Tradeoffs and Performance Results of the Banded PRISM Eigensolver", Eighth SIAM Conference on Parallel Processing for Scientific Computing, March 1997 as compressed postscript or postscript.