منابع مشابه
Compressed Modular Matrix Multiplication
Matrices of integers modulo a small prime can be compressed by storing several entries into a single machine word. Modular addition is performed by addition and possibly subtraction of a word containing several times the modulus. We show how modular multiplication can also be performed. In terms of arithmetic operations, the gain over classical matrix multiplication is equal to the number of in...
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Efficient parallel multiplication of sparse matrices is key to enabling many large-scale calculations. This article presents the DBCSR (Distributed Block Compressed Sparse Row) library for scalable sparse matrix-matrix multiplication and its use in the CP2K program for linear-scaling quantum-chemical calculations. The library combines several approaches to implement sparse matrix multiplication...
متن کاملA note on compressed sensing and the complexity of matrix multiplication
We consider the conjectured O(N2+ ) time complexity of multiplying any two N × N matrices A and B. Our main result is a deterministic Compressed Sensing (CS) algorithm that both rapidly and accurately computes A · B provided that the resulting matrix product is sparse/compressible. As a consequence of our main result we increase the class of matrices A, for any given N × N matrix B, which allow...
متن کاملFast Matrix Multiplication
We give an overview of the history of fast algorithms for matrix multiplication. Along the way, we look at some other fundamental problems in algebraic complexity like polynomial evaluation. This exposition is self-contained. To make it accessible to a broad audience, we only assume a minimal mathematical background: basic linear algebra, familiarity with polynomials in several variables over r...
متن کاملMatrix Multiplication I
These notes are based on a lecture given at the Toronto Student Seminar on February 2, 2012. The material is taken mostly from the book Algebraic Complexity Theory [ACT] and the lecture notes by Bläser and Bendun [Blä]. Starred sections are the ones I didn't have time to cover. This lecture discusses the problem of multiplying two square matrices. We will be working in the algebraic complexity ...
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ژورنال
عنوان ژورنال: ACM Transactions on Computation Theory
سال: 2013
ISSN: 1942-3454,1942-3462
DOI: 10.1145/2493252.2493254