Robert A. van de Geijn. Using PLAPACK: Parallel Linear Algebra Package. The MIT Press, 1997.
Robert A. van de Geijn and Enrique S. Quintana-Ortí. The Science of Programming Matrix Computations. www.lulu.com, 2008.
Robert A. van de Geijn (editor). A Systematic Approach to Matrix Computations: A collection of papers from ACM TOMS. In preparation.
Field G. Van Zee. libflame: The Complete Reference. www.lulu.com, 2009. In preparation.
John A. Gunnels. "A Systematic Approach to the Design and Analysis of Linear Algebra Algorithms." The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-01-44. December 2001.
Paolo Bientinesi. "Mechanical Derivation and Systematic Analysis of Correct Linear Algebra Algorithms." The University of Texas at Austin, Department of Computer Sciences. August 2006.
Jack Poulson. "Formalized Parallel Dense Linear Algebra and its Application to the Generalized Eigenvalue Problem." Masters Thesis. The University of Texas at Austin, Department of Aerospace Engineering. May 2009. (Supervised by Prof. Jeffrey K. Bennighof)
John A. Gunnels, Fred G. Gustavson, Greg M. Henry, and Robert A. van de Geijn. "FLAME: Formal Linear Algebra Methods Environment." ACM Transactions on Mathematical Software , 27(4):422-455, December 2001.
Postscript (gzipped)
Enrique S. Quintana-Ortí and Robert van de Geijn, "Formal Derivation of Algorithms: The Triangular Sylvester Equation." ACM Transactions on Mathematical Software, (29)2, June 2003.
Postscript (gzipped)
Note: this journal version is updated extensively from FLAME Working Note #5.Paolo Bientinesi, John A. Gunnels, Margaret E. Myers, Enrique S. Quintana-Ortí, and Robert van de Geijn. "The Science of Deriving Dense Linear Algebra Algorithms." ACM Transactions on Mathematical Software, 31(1):1-26, March 2005.
Postscript (Draft)
Paolo Bientinesi, Enrique S. Quintana-Ortí, and Robert van de Geijn. "Representing Linear Algebra Algorithms in Code: The FLAME APIs. ACM Transactions on Mathematical Software, 31(1):27-59, March 2005.
Paolo Bientinesi, Inderjit S. Dhillon, and Robert A. van de Geijn. "A Parallel Eigensolver for Dense Symmetric Matrices Based on Multiple Relatively Robust Representations. SIAM Journal on Scientific Computing , 27(1), 2005.
Brian Gunter and Robert van de Geijn. "Parallel Out-of-Core Computation and Updating of the QR Factorization." ACM Transactions on Mathematical Software, 31(1):60-78, March 2005.
Postscript (gzipped)
Thierry Joffrain, Tze Meng Low, Enrique S. Quintana-Ortí, Robert van de Geijn, and Field Van Zee. "Accumulating Householder Transformations, Revisited." ACM Transactions on Mathematical Software, 32 (2):169-179.
Gregorio Quintana-Ortí and Robert van de Geijn. "Improving the Performance of Reduction to Hessenberg Form. ACM Transactions on Mathematical Software, 32(2):180-194.
Postscript (final revision)
Kazushige Goto and Robert A. van de Geijn. "Anatomy of High-Performance Matrix Multiplication," ACM Transactions on Mathematical Software, 34(3): Article 12, 25 pages, May 2008.
Paolo Bientinesi, Brian Gunter, and Robert van de Geijn. "Families of Algorithms Related to the Inversion of a Symmetric Positive Definite Matrix. ACM Transactions on Mathematical Software, 31(1), pp. 60-78, March 2005.
Paolo Bientinesi and Robert van de Geijn. "Representing Dense Linear Algebra Algorithms: A Farewell to Indices." Target journal to be determined.
Postscript (Draft)
PDF (Draft)
H. Carter Edwards and Robert A. van de Geijn. "Application Interface to Parallel Dense Matrix Libraries: Just let me solve my problem!" Concurrency and Computation: Practice and Experience, Accepted pending modifications (?).
PDF (Draft)
Kazushige Goto and Robert van de Geijn. "High-Performance Implementation of the Level-3 BLAS." ACM Transactions on Mathematical Software, 35(1): Article 4, 14 pages, July 2008.
Enrique S. Quintana-Ortí and Robert van de Geijn. "Updating an LU Factorization with Pivoting." ACM Transactions on Mathematical Software, 35(2): Article 11, 16 pages, July 2008.
Ernie Chan, Marcel Heimlich, Avi Purkayastha, and Robert van de Geijn. "Collective communication: theory, practice, and experience." Concurrency and Computation: Practice and Experience, 19(13):1749--1783, July 5, 2007.
PDF (FLAME Working Note #22)
Field G. Van Zee, Paolo Bientinesi, Tze Meng Low, and Robert A. van de Geijn. "Scalable Parallelization of FLAME Code via the Workqueuing Model." ACM Transactions on Mathematical Software, 34(2), 29 pages, March 2008.
Gregorio Quintana-Ortí, Enrique S. Quintana-Ortí, Robert A. van de Geijn, Field G. Van Zee, and Ernie Chan. "Programming Matrix Algorithms-by-Blocks for Thread-Level Parallelism." ACM Transactions on Mathematical Software, to appear.
Paolo Bientinesi and Robert A. van de Geijn. "A Goal-Oriented and Modular Approach to Stability Analysis." SIAM Journal on Matrix Analysis and Applications. Submitted.
Richard M. Veras, Jonathan S. Monette, Enrique S. Quintana-Ortí, and Robert A. van de Geijn. "Transforming Linear Algebra Libraries: From Abstraction to High Performance." ACM Transactions on Mathematical Software, submitted.
Field G. Van Zee, Ernie Chan, Robert van de Geijn, Enrique S. Quintana-Ortí, and Gregorio Quintana-Ortí. "Introducing: The libflame Library for Dense Matrix Computations." CiSE, submitted.
John Gunnels and Robert van de Geijn, "Formal Methods for High-Performance Linear Algebra Libraries," in The Architecture of Scientific Software, (R. F. Boisvert and P. T. Tang, editors), pp. 193-210, Kluwer Academic Press, 2001.
John A. Gunnels, Daniel S. Katz, Enrique S. Quintana-Ortí, and Robert van de Geijn. "Fault-Tolerant High-Performance Matrix-Matrix Multiplication: Theory and Practice," The International Conference for Dependable Systems and Networks (DSN-2001), pp. 47-56, July 2-4, 2001.
John A. Gunnels, Greg M. Henry, and Robert A. van de Geijn. "A Family of High-Performance Matrix Algorithms." In Computational Science - 2001, Part I, Lecture Notes in Computer Science 2073, pp. 51-60, Springer, 2001.
Thierry Joffrain, Enrique S. Quintana-Ortí, and Robert A. van de Geijn. "Rapid Development of High-Performance Out-of-Core Solvers," PARA 2004, LNCS 3732, pp. 413--422, 2005. Early draft:
Paolo Bientinesi, Sergey Kolos, and Robert A. van de Geijn, "Automatic Derivation of Linear Algebra Algorithms with Application to Control Theory," PARA 2004, LNCS 3732, pp. 385--394, 2005. Early draft:
Paolo Bientinesi, John Gunnels, Fred Gustavson, Greg Henry, Margaret Myers, Enrique S. Quintana-Ortí, and Robert A. van de Geijn,"Rapid Development of High-Performance Linear Algebra Libraries," PARA 2004, LNCS 3732, pp. 376--384, 2005. Early draft:
John Gunnels, Fred Gustavson, Greg Henry, and Robert A. van de Geijn, "A Family of High-Performance Matrix Multiplication Algorithms," PARA 2004, LNCS 3732, pp. 2256-265, 2005.
Tze Meng Low, Robert van de Geijn, and Field Van Zee. "Extracting SMP Parallelism for Dense Linear Algebra Algorithms from High-Level Specifications." PPoPP05.
Paolo Bientinesi and Robert van de Geijn. "Formal Correctness and Stability of Linear Algebra Algorithms." IMACS05.
Ernie Chan, Enrique S. Quintana-Ortí, Gregorio Quintana-Ortí, and Robert van de Geijn. "SuperMatrix Out-of-Order Scheduling of Matrix Operations for SMP and Multi-Core Architectures." SPAA '07: Proceedings of the Nineteenth ACM Symposium on Parallelism in Algorithms and Architectures. pp. 116-125. 2007.
Bryan Marker, Field Van Zee, Kazushige Goto, Gregorio Quintana-Ortí, Robert van de Geijn. "Toward Scalable Matrix Multiply on Multithreaded Architectures." Proceedings of European Conference on Parallel and Distributed Computing, pp. 748-757, Rennes, France, August 2007.
Ernie Chan, Field G. Van Zee, Enrique S. Quintana-Ortí, Gregorio Quintana-Ortí, Robert van de Geijn. "Satisfying your Dependencies with SuperMatrix." Proceedings of IEEE Cluster Computing 2007, pp. 91 - 99, Austin, Texas, September 2007.
Gregorio Quintana-Ortí, Enrique S. Quintana-Ortí, Ernie Chan, Field G. Van Zee, and Robert A. van de Geijn. "Scheduling of QR factorization algorithms on SMP and multi-core architectures." Proceedings of the 16th Euromicro International Conference on Parallel, Distributed and network-based Processing, Toulouse, France, February 2008.
Ernie Chan, Field G. Van Zee, Paolo Bientinesi, Enrique S. Quintana-Ortí, Gregorio Quintana-Ortí, and Robert van de Geijn. "SuperMatrix: A Multithreaded Runtime Scheduling System for Algorithms-by-Blocks." Proceedings of 2008 ACM SIGPLAN Symposium on Principles and Practices of Parallel Programming, p. 123-132, Salt Lake City, Utah, February 2008.
Gregorio Quintana-Ortí, Enrique S. Quintana-Ortí, Ernie Chan, Robert van de Geijn, and Field G. Van Zee. "Design of Scalable Dense Linear Algebra Libraries for Multithreaded Architectures: the LU Factorization." Proceedings of the Workshop on Multithreaded Architectures and Applications, Miami, Florida, April 2008.
Gregorio Quintana-Ortí, Enrique S. Quintana-Ortí, Alfredo Remón, and Robert A. van de Geijn. "An Algorithm-by-Blocks for SuperMatrix Band Cholesky Factorization." Lecture Notes in Computer Science 5336, 8th Int. Meeting on High Performance Computing for Computational Science - VECPAR2008 (J.M. Laginha M. Palma, P.R. Amestoy, M. Daydé, M. Mattoso, J. Correia, Eds.), pp. 228-239, Toulouse, France, 2008
Jeff Diamond, Behnam Robatmili, Stephen W. Keckler, Robert van de Geijn, Kazushige Goto, Doug Burger. "High Performance Dense Linear Algebra on a Spatially Distributed Processor." Proceedings of 2008 ACM SIGPLAN Symposium on Principles and Practices of Parallel Programming, Salt Lake City, Utah, February 2008.
Gregorio Quintana-Ortí, Francisco D. Igual, Enrique S. Quintana-Ortí, Robert van de Geijn. "Solving Dense Linear Algebra Problems on Platforms with Multiple Hardware Accelerators." Proceedings of 2009 ACM SIGPLAN Symposium on Principles and Practices of Parallel Programming, Raleigh, North Carolina, February 2009.
María Jesús Zafont, Alberto Martín, Francisco D. Igual, and Enrique S. Quintana-Ortí. "Fast Development of Dense Linear Algebra Codes on Graphics Processors." 14th International Workshop on High-Level Parallel Programming Models and Supportive Environments, 2009. Rome, Italy. To apear.
Mercedes Marqués, Gregorio Quintana-Ortí, Enrique S. Quintana-Ortí, and Robert van de Geijn. "Using Graphics Processors to Accelerate the Solution of Out-of-Core Linear Systems"8th IEEE International Symposium on Parallel and Distributed Computing, Lisbon (Portugal), 2009. To appear.
Mercedes Marqués, Gregorio Quintana-Ortí, Enrique S. Quintana-Ortí, and Robert van de Geijn. "Solving ``Large'' Dense Matrix Problems on Multi-Core Processors and GPUs" 10th IEEE International Workshop on Parallel and Distributed Scientific and Engineering Computing - PDSEC'09. Roma (Italia). 2009. To appear.
Mercedes Marqués, Gregorio Quintana-Ortí, Enrique S. Quintana-Ortí, and Robert van de Geijn. "Out-of-Core Computation of the QR Factorization on Multi-Core Processors." Euro-Par 2009. Accepted.
John Gunnels, Greg Henry, and Robert van de Geijn. "Formal Linear Algebra Methods Environment (FLAME): Overview." FLAME Working Note #1. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-2000-28. November 2000.
John A. Gunnels, Daniel S. Katz, Enrique S. Quintana-Ortí, and Robert van de Geijn. "Fault-Tolerant High-Performance Matrix-Matrix Multiplication," FLAME Working Note #2. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-2000-34. December 2000.
John Gunnels and Robert van de Geijn. "Developing Linear Algebra Algorithms: A Collection of Class Projects." FLAME Working Note #3. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-2001-19. May 2001.
John Gunnels, Greg Henry, and Robert van de Geijn. "High-Performance Matrix Multiplication Algorithms for Architectures with Hierarchical Memories." FLAME Working Note #4. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-2001-22. June 2001.
Enrique S. Quintana-Ortí and Robert van de Geijn. "Formal Derivation of Algorithms: The Triangular Sylvester Equation." FLAME Working Note #5. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-2001-35. Sept. 2001.
John A. Gunnels. "A Systematic Approach to the Design and Analysis of Linear Algebra Algorithms." Ph.D. Dissertation. FLAME Working Note #6, The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-2001-44. Nov. 2001.
Greg M. Henry. "Flexible High-Performance Matrix Multiply via a Self-Modifying Runtime Code." FLAME Working Note #7. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-2001-46. Dec. 2001.
Paolo Bientinesi, John A. Gunnels, Margaret E. Myers, Enrique S. Quintana-Ortí, and Robert van de Geijn. "The Science of Deriving Dense Linear Algebra Algorithms." FLAME Working Note #8. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-2002-53. Sept. 2002.
Kazushige Goto and Robert van de Geijn. On Reducing TLB Misses in Matrix Multiplication. FLAME Working Note #9. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-2002-55. Nov. 2002.
Robert A. van de Geijn. "Representing Linear Algebra Algorithms in Code: The FLAME API." FLAME Working Note #10. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-2003-01. Jan. 2003.
Paolo Bientinesi, Enrique S. Quintana-Ortí, and Robert van de Geijn. "FLAME@lab: A Farewell to Indices." FLAME Working Note #11. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-2003-11. April 2003.
Tze Meng Low and Robert van de Geijn. "An API for Manipulating Matrices Stored by Blocks." FLAME Working Note #12. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-2004-15. May 2004.
Thierry Joffrain, Tze Meng Low, Enrique S. Quintana-Ortí, Robert van de Geijn, and Field Van Zee. "On Accumulating Householder Transformations." FLAME Working Note #13. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-2004-43. Oct 2004.
Gregorio Quintana-Ortí and Robert van de Geijn. "Improving the Performance of Reduction to Hessenberg Form." FLAME Working Note #14. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-2004-44. Oct 2004.
PDF (not available)
Tze Meng Low, Kent Milfeld, Robert van de Geijn, and Field Van Zee. "Parallelizing FLAME Code with OpenMP Task Queues." FLAME Working Note #15. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-2004-50.
Paolo Bientinesi, Kazushige Goto, Tze Meng Low, Enrique S. Quintana-Ortí, Robert van de Geijn, and Field Van Zee. "FLAME 2005 Prospectus: Towards the Final Generation of Dense Linear Algebra Libraries." FLAME Working Note #16. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-2005-15.
Paolo Bientinesi and Robert van de Geijn. "Representing Dense Linear Algebra Algorithms: A Farewell to Indices." FLAME Working Note #17. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-2006-10.
H. Carter Edwards and Robert A. van de Geijn. "Application Interface to Parallel Dense Matrix Libraries: Just let me solve my problem!" FLAME Working Note #18. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-2006-15.
Paolo Bientinesi, Brian Gunter, and Robert van de Geijn, "Families of Algorithms Related to the Inversion of a Symmetric Positive Definite Matrix." FLAME Working Note #19. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-2006-20.
Kazushige Goto and Robert van de Geijn. "High-Performance Implementation of the Level-3 BLAS." FLAME Working Note #20. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-2006-23.
Enrique S. Quintana-Ortí and Robert van de Geijn. "Updating an LU Factorization with Pivoting." FLAME Working Note #21. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-2006-42.
Ernie Chan, Marcel Heimlich, Avijit Purkayastha, and Robert van de Geijn. "Collective Communication: Theory, Practice, and Experience." FLAME Working Note #22. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-06-44. September 26, 2006.
Ernie Chan, Enrique S. Quintana-Ortí, Gregorio Quintana-Ortí, and Robert van de Geijn. "SuperMatrix Out-of-Order Scheduling of Matrix Operations for SMP and Multi-Core Architectures." FLAME Working Note #23. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-06-67. December 18, 2006.
Gregorio Quintana-Ortí, Enrique S. Quintana-Ortí, Ernie Chan, Field G. Van Zee, and Robert van de Geijn. "Scheduling of QR factorization algorithms on SMP and multi-core architectures." FLAME Working Note #24. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-07-37. July 31, 2007.
Ernie Chan, Field G. Van Zee, Paolo Bientinesi, Enrique S. Quintana-Ortí, Gregorio Quintana-Ortí, and Robert van de Geijn. "SuperMatrix: A Multithreaded Runtime Scheduling System for Algorithms-by-Blocks." FLAME Working Note #25. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-07-41. August 22, 2007.
Gregorio Quintana-Ortí, Enrique S. Quintana-Ortí, Ernie Chan, Robert van de Geijn, Field G. Van Zee. "Design and Scheduling of an Algorithm-by-Blocks for LU Factorization on Multithreaded Architectures." FLAME Working Note #26. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-07-50. September 19, 2007.
Gregorio Quintana-Ortí, Enrique S. Quintana-Ortí, Alfredo Remon, Robert van de Geijn. "SuperMatrix for the Factorization of Band Matrices." FLAME Working Note #27. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-07-51. September 24, 2007.
Bryan Marker. "On Composing Matrix Multiplication from Kernels." FLAME Working Note #28. The University of Texas at Austin, Department of Computer Sciences. Report# HR-07-32 (honors thesis). Spring 2007. 21 pages.
Gregorio Quintana-Ortí, Enrique S. Quintana-Ortí, Ernie Chan, Field G. Van Zee, and Robert van de Geijn. "Programming Algorithms-by-Blocks for Matrix Computations on Multithreaded Architectures." FLAME Working Note #29. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-08-04. January 15, 2008.
Sergio Barrachina, Maribel Castillo, Francisco D. Igual, Rafael Mayo, Enrique S. Quintana-Ortí. "FLAG@lab: An M-script API for Linear Algebra Operations on Graphics Processors." FLAME Working Note #30. Universidad Jaume I, Depto. de Ingenieria y Ciencia de Computadores. Technical Report ICC 01-02-2008. February 14, 2008.
Maribel Castillo, Ernie Chan, Francisco D. Igual, Rafael Mayo, Enrique S. Quintana-Ortí, Gregorio Quintana-Ortí, Robert van de Geijn, Field G. Van Zee. "Making Programming Synonymous with Programming for Linear Algebra Libraries." FLAME Working Note #31. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-08-20. April 17, 2008.
Gregorio Quintana-Ortí, Francisco D. Igual, Enrique S. Quintana-Ortí, Robert van de Geijn. "Solving Dense Linear Algebra Problems on Platforms with Multiple Hardware Accelerators." FLAME Working Note #32. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-08-22. May 9, 2008.
Paolo Bientinesi and Robert A. van de Geijn. "The Science of Deriving Stability Analyses." FLAME Working Note #33. Aachen Institute for Computational Engineering Sciences, RWTH Aachen. TR AICES-2008-2. November 2008.
Robert van de Geijn. "Beautiful Parallel Code: Evolution vs. Intelligent Design." Presented at Supercomputing 2008 Workshop on Node Level Parallelism for Large Scale Supercomputers, Austin, Texas, November 2008. FLAME Working Note #34. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-08-46. Nov. 21, 2008.
Richard Veras, Jonathan Monette, Enrique Quintana-Ortí, and Robert van de Geijn. "FLAMES2S: From Abstraction to High Performance." FLAME Working Note #35. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-08-49. Dec. 14, 2008.
Mercedes Marqués, Gregorio Quintana-Ortí, Enrique S. Quintana-Ortí, and Robert van de Geijn. "Solving ``Large'' Dense Matrix Problems on Multi-Core Processors and GPUs" FLAME Working Note #36. Universidad Jaume I, Depto. de Ingenieria y Ciencia de Computadores. Technical Report ICC 01-01-2009. Jan. 7, 2009.
Francisco D. Igual, Gregorio Quintana-Ortí, and Robert van de Geijn. "Level-3 BLAS on a GPU: Picking the Low Hanging Fruit " FLAME Working Note #37. Universidad Jaume I, Depto. de Ingenieria y Ciencia de Computadores. Technical Report DICC 2009-04-01. April 30, 2009, Updated May 21, 2009.
Ernie Chan, Jim Nagle, Robert van de Geijn, and Field G. Van Zee. "Transforming Linear Algebra Libraries: From Abstraction to Parallelism." FLAME Working Note #38. The University of Texas at Austin, Department of Computer Sciences. Technical Report TR-09-17. May 27, 2009.
Paolo Bientinesi, Victor Eijkhout, Kyungjoo Kim, Jason Kurtz and Robert van de Geijn. "Sparse Direct Factorizations through Unassembled Hyper-Matrices." The University of Texas at Austin, Texas Advanced Computing Center. Technical Report TR-07-02. Submitted to Computer Methods in Applied Mechanics and Engineering.
Rosa M. Badia, Jose R. Herrero, Jesus Labarta, Josep M. Perez, Enrique S. Quintana-Ortí and Gregorio Quintana-Ortí. "Parallelizing dense and banded linear algebra libraries using SMPSs." Departament of Computer Architecture, Universitat Politecnica de Catalunya. Technical Report UPC-DAC-RR-2008-64. 2008.