ReportDOI
Algorithms for matrix multiplication
TLDR
Strassen''s and Winograd''s algorithms for matrix multiplication are investigated and compared with the normal algorithm, and it is shown that scaling is essential for numerical accuracy using Winog rad''s method.Abstract:
Strassen''s and Winograd''s algorithms for matrix multiplication are investigated and compared with the normal algorithm. Floating-point error bounds are obtained, and it is shown that scaling is essential for numerical accuracy using Winograd''s method. In practical cases Winograd''s method appears to be slightly faster than the other two methods, but the gain is, at most, about 20%. Finally, an attempt to generalize Strassen''s method is described.read more
Citations
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Journal ArticleDOI
Performance of Processor-Memory Interconnections for Multiprocessors
TL;DR: The analysis shows that delta networks have a far better performance per cost than crossbars in large multiprocessing systems.
Journal ArticleDOI
Fast linear algebra is stable
TL;DR: It is shown that essentially all standard linear algebra operations, including LU decompositions, QR decomposition, linear equation solving, matrix inversion, solving least squares problems, (generalized) eigenvalue problems and the singular value decomposition can also be done stably (in a normwise sense) in O(nω+η) operations.
Journal ArticleDOI
Fast linear algebra is stable
TL;DR: In this article, it was shown that a large class of fast recursive matrix multiplication algorithms are stable in a norm-wise sense, including LU decomposition, QR decomposition and linear equation solving, matrix inversion, solving least squares problems, eigenvalue problems and singular value decomposition.
Proceedings ArticleDOI
Implementation of Strassen's Algorithm for Matrix Multiplication
TL;DR: The implementation is designed to be used in place of DGEMM, the Level 3 BLAS matrix mulitplication routine, and reconfirms that Strassen's algorithm is practical for realistic size matrices.
Journal ArticleDOI
A noncommutative algorithm for multiplying $3 \times 3$ matrices using 23 multiplications
TL;DR: A noncommutative algorithm performs matrix multiplication without requiring the matrix elements to be commutative under the operation of multiplication, most desirable since it can be employed to multiply two matrices whose elements are themselves matrices.
References
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