The Better Accuracy of Strassen-Winograd Algorithms (FastMMW)

Impact of mixed-parallelism on parallel implementations of the Strassen and Winograd matrix multiplication algorithms

Performance evaluation of multiple precision matrix multiplications using parallelized Strassen and Winograd algorithms

It is well known that Strassen and Winograd algorithms can reduce the computational costs associated with dense matrix multiplication. We have already shown that they are also very effective for software-based multiple precision floating-point arithmetic environments such as the MPFR/GMP library. In this paper, we show that we can obtain the same effectiveness for double-double (DD) and quadrup...

OURAGAN WHITE PAPER Mixed Parallel Implementations of the Top Level Step of Strassen and Winograd Matrix Multiplication Algorithms

This paper presents parallel implementations of the top level of Strassen and Winograd algorithms for matrix multiplication that use mixed-parallelism, i.e., simultaneous exploitation of dataand task-parallelism. This paradigm allows a better task placement and reduces the communication costs. A comparison with the ScaLAPACK implementation of the matrix multiplication is given. We present a the...

Winograd ' s Short DFT Algorithms ∗

In 1976, S. Winograd [20] presented a new DFT algorithm which had signi cantly fewer multiplications than the Cooley-Tukey FFT which had been published eleven years earlier. This new Winograd Fourier Transform Algorithm (WFTA) is based on the typeone index map from Multidimensional Index Mapping with each of the relatively prime length short DFT's calculated by very e cient special algorithms. ...

Improving accuracy of Winograd convolution for DNNs

Modern deep neural networks (DNNs) spend a large amount of their execution time computing convolutions. Winograd's minimal algorithm for small convolutions can greatly reduce the number of arithmetic operations. However, a large reduction in floating point (FP) operations in these algorithms can result in significantly reduced FP accuracy of the result. In this paper we propose several methods ...