Optimization techniques for small matrix multiplication

Optimization Methods for Sparse Matrix-Vector Multiplication

A lightweight optimization selection method for Sparse Matrix-Vector Multiplication

In this paper, we propose an optimization selection methodology for the ubiquitous sparse matrix-vector multiplication (SpMV) kernel. We propose two models that attempt to identify the major performance bottleneck of the kernel for every instance of the problem and then select an appropriate optimization to tackle it. Our first model requires online profiling of the input matrix in order to det...

Optimization of sparse matrix-vector multiplication using reordering techniques on GPUs

It is well-known that reordering techniques applied to sparse matrices are common strategies to improve the performance of sparse matrix operations, and particularly, the sparse matrix vector multiplication (SpMV) on CPUs. In this paper, we have evaluated some of the most successful reordering techniques on two different GPUs. In addition, in our study a number of sparse matrix storage formats ...

Algorithms for Matrix Multiplication

Strassen’s and Winograd’s algorithms for n × n matrix multiplication are investigated and compared with the normal algorithm. The normal algorithm requires n3 + O(n2) multiplications and about the same number of additions. Winograd’s algorithm almost halves the number of multiplications at the expense of more additions. Strassen’s algorithm reduces the total number of operations to O(n2.82) by ...

Fast matrix multiplication techniques based on the Adleman-Lipton model

Abstract. On distributed memory electronic computers, the implementation and association of fast parallel matrix multiplication algorithms has yielded astounding results and insights. In this discourse, we use the tools of molecular biology to demonstrate the theoretical encoding of Strassen’s fast matrix multiplication algorithm with DNA based on an n-moduli set in the residue number system, t...