Coded distributed computing was recently introduced to mitigate the effect of stragglers on systems. This paper combines ideas approximate and coded further accelerate computation. We propose successive approximation coding (SAC) techniques that realize a tradeoff between accuracy speed, allowing system produce approximations increase in over time. If sufficient number compute nodes finish thei...

Matrix multiplication has been implemented in various programming languages, and improved performance reported many articles under settings. is of paramount interest to machine learning, a lightweight matrix-based key management protocol for IoT networks, animation, so on. There always need an terms algorithm implementation. In this work, the authors compared run times matrix popular languages ...

Partitioned global address space (PGAS) languages, such as Unified Parallel C (UPC) have the promise of being productive. Due to the shared address space view that they provide, they make distributing data and operating on ghost zones relatively easy. Meanwhile, they provide thread-data affinity that can enable locality exploitation. In this paper, we are considering sparse matrix multiplicatio...

Approximating the product of two matrices with random sampling or random projection methods is a fundamental operation that is of interest in and of itself as well as since it is used in a critical way as a primitive for many RandNLA algorithms. In this class, we will introduce a basic algorithm; and in this and the next few classes, we will discusses several related methods. Here is the readin...

We introduced matrices as a computational tool for working with linear transformations between finitely generated vector spaces. The general properties of linear transformations and the algebraic operations on them — addition, multiplication by scalars and composition — enabled us to define corresponding algebraic operations on matrices — matrix addition, multiplication by scalars and matrix mu...

In this paper we present an adaptable fast matrix multiplication (AFMM) algorithm , for two nxn dense matrices which computes the product matrix with average complexity Tavg(n) = μ’d1d2n with the acknowledgement that the average count is obtained for addition as the basic operation rather than multiplication which is probably the unquestionable choice for basic operation in existing matrix mult...

Given N matrices A1, A2, ..., AN of size N × N, the matrix chain product problem is to compute A1 × A2 × ...× AN. Given an N × N matrix A, the matrix powers problem is to calculate the first N powers of A, i.e., A, A, A, ..., A. Both problems are important in conducting many matrix manipulations such as computing the characteristic polynomial, determinant, rank, and inverse of a matrix, and in ...

Strassen’s algorithm is an algorithm for computing matrix-matrix multiplication using only 7 multiplications rather than the usual 8. Recent advances have shown the benefit of using Strassen’s algorithm to improve the performance of general matrix-matrix multiplication (GEMM) for matrices of varying shapes and sizes. These advances have created an opportunity to incorporate Strassen’s algorithm...

In the past few years, successive improvements of the asymptotic complexity of square matrix multiplication have been obtained by developing novel methods to analyze the powers of the Coppersmith-Winograd tensor, a basic construction introduced thirty years ago. In this paper we show how to generalize this approach to make progress on the complexity of rectangular matrix multiplication as well,...