Matrix multiplicationParallel algorithmsStrassen'sWinograd's algorithmSeveral implementations of matrix multiplication (MMUL) in Fortran and VAX assembly language are discussed. On a VAX-11/780 computer, the mos
Matrix multiplicationParallel algorithmsStrassen'sWinograd's algorithmATLAS, created by a group of researchers/Jack Dongarra (UTK) Goto came 2002 to Texas to work with R. van de Geijn turned his attention to optimizing the speed of the Pentium 4 "When computer scientists at the University at ...
Abstract. The fast matrix multiplication algorithm by Strassen is used to obtain the triangular factorization of a permutation of any nonsingular matrix of ordern in operations, and, hence, the inverse of any nonsingular matrix in 1. Introduction. Strassen [3] has given an algorithm using no...
The ambition of this monograph is to show the methods of constructing fast matrix multiplication algorithms, and their applications, in an intelligible way, accessible not only to mathematicians. The scope and coverage of the book are comprehensive and constructive, and the analyses and algorithms can...
Interestingly, we prove this by way of a combinatorial construction called \\emph{uniquely solvable puzzles} that was at the heart of Coppersmith and Winograd's renowned matrix multiplication algorithm.doi:10.4230/LIPIcs.APPROX-RANDOM.2014.669Fu, Hu...
For m ≤ n 1.68 , the new algorithm is also faster than the best known matrix multiplication algorithm for dense matrices which uses O ( n 2.38 ) algebraic operations. The new algorithm is obtained using a surprisingly straightforward combination of a simple combinatorial idea and existing fast ...
For m ≤ n 1.68 , the new algorithm is also faster than the best known matrix multiplication algorithm for dense matrices which uses O ( n 2.38 ) algebraic operations. The new algorithm is obtained using a surprisingly straightforward combination of a simple combinatorial idea and existing fast ...
some brute-force algorithm has been proposed, which is exact but time-consuming. The ant colony optimization is a randomized heuristic algorithm and finds extensive applications in many fields. We use it to solve the problem of searching for three subsets of a given group such that they satisfy...
Computation of central moments up to fourth order using an online algorithm (Spicer, 1972). Evaluation of a real general matrix polynomial using Horner's scheme. Fast computation of Hadamard product using unrolled loops. Gauss-Seidel, Jacobi and conjugate gradients (CG) iterative methods for solvin...
We design two nondeterministic algorithms for matrix multiplication. Both algorithms are based on derandomization of Freivalds’ algorithm for verification of matrix products. The first algorithm works with real numbers and its time complexity on Real RAMs isO(n2logn). The second one is of the same...