A framework for high-performance matrix multiplication based on hierarchical abstractions, algorithms and optimized low-level kernels

Concurrency and Computation: Practice and Experience

Volumn 14, Issue 10, 2002, Pages 805-839

  Valsalam, Vinod ^a   Skjellum, Anthony ^a,b  

^a MISSISSIPPI STATE UNIVERSITY   (United States)

^b MISSISSIPPI STATE UNIVERSITY   (United States)

Author keywords

Hierarchical matrix storage; Kernel interface; Matrix multiplication; Morton order; Polyalgorithms; Strassen's algorithm

Indexed keywords

ALGORITHMS; HIERARCHICAL SYSTEMS; INTERFACES (COMPUTER); OBJECT ORIENTED PROGRAMMING; OPTIMIZATION; PROGRAM COMPILERS; REDUCED INSTRUCTION SET COMPUTING;

MATRIX MULTIPLICATION;

MATRIX ALGEBRA;

EID: 0037173976     PISSN: 15320626     EISSN: None     Source Type: Journal    
DOI: 10.1002/cpe.630     Document Type: Article

References (63)

1. Iteration space tiling for memory hierarchies
2. Impact of hierarchical memory systems on linear algebra algorithm design
3. The cache performance and optimizations of blocked algorithms
4. A data locality optimizing algorithm
5. Hierarchical blocking and data flow analysis for numerical linear algebra
6. Exploiting functional parallelism of POWER2 to design high-performance numerical algorithms
7. MOB forms: A class of multilevel block algorithms for dense linear algebra operations
8. A set of level 3 basic linear algebra subprograms
9. Emmerald: A fast matrix-matrix multiply using Intel SIMD technology
10. Auto-blocking matrix multiplication or tracking BLAS3 performance with source code
11. Recursive array layouts and fast parallel matrix multiplication
12. Recursive blocked data formats and BLAS's for dense linear algebra algorithms
13. Recursion leads to automatic variable blocking for dense linear algebra algorithms
14. LAWRA - Linear algebra with recursive algorithms
15. Minimal-storage high-performance Cholesky factorization via blocking and recursion
16. New generalized data structures for matrices lead to a variety of high performance algorithms
17. Nonlinear array layouts for hierarchical memory systems
18. Optimizing matrix multiply using PHiPAC: A portable, high-performance, ANSI C coding methodology
19. The matrix template library: A generic programming approach to high performance numerical linear algebra
20. The matrix template library: A unifying framework for numerical linear algebra
21. The parallel mathematical libraries project (PMLP): Overview, design innovations and preliminary results
22. The parallel mathematical libraries project (PMLP) - A next generation scalable, sparse, object-oriented, mathematical library suite
23. Gaussian elimination is not optimal
24. Exploiting fast matrix multiplication within the level 3 BLAS
25. GEMMW: A portable level 3 BLAS winograd variant of Strassen's matrix-matrix multiply algorithm
26. Implementation of Strassen's algorithm for matrix multiplication
27. Architecture-efficient Strassen's matrix multiplication: A case study of divide-and-conquer algorithms
28. Tuning Strassen's matrix multiplication for memory efficiency
29. Ahnentafel indexing into morton-ordered arrays' or matrix locality for free
30. A poly-algorithm for parallel dense matrix multiplication on two-dimensional process grid topologies
31. A flexible class of parallel matrix multiplication algorithms
32. A three-dimensional approach to parallel matrix multiplication
33. Finding neighbors of equal size in linear quadtrees and octrees in constant time
34. Integer dilation and contraction for quadtrees and octrees
35. A tensor product formulation of Strassen's matrix multiplication algorithm
36. Efficient procedures for using matrix algorithms
37. Standard sequential mathematical libraries: Promises and pitfalls, opportunities and challenges
38. A rational approach to portable high performance: The basic linear algebra instruction set (BLAIS) and the fixed algorithm size template (FAST) library
39. Formal linear algebra methods environment (FLAME) overview
40. High performance software on intel pentium pro processors or micro-ops to TeraFLOPS
41. Superscalar GEMM-based level 3 BLAS - The on-going evolution of a portable and high-performance library