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Matrix Multiplication

by List Of (dominic Garmo, Raymon Benjamin, Tiantian Ma, Swain Dakho
"... Abstract- In the following project we created a simple 2x2 and 3x3 matrix multiplier. The user can input 4 bit numbers that will be displayed on the seven segment display. The user will know where the answer is located on the matrix by the LED’s displaying the position on the matrix. I. ..."
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Abstract- In the following project we created a simple 2x2 and 3x3 matrix multiplier. The user can input 4 bit numbers that will be displayed on the seven segment display. The user will know where the answer is located on the matrix by the LED’s displaying the position on the matrix. I.

Fast Sparse Matrix Multiplication

by Raphael Yuster, Uri Zwick , 2004
"... Let A and B two n n matrices over a ring R (e.g., the reals or the integers) each containing at most m non-zero elements. We present a new algorithm that multiplies A and B using O(m ) algebraic operations (i.e., multiplications, additions and subtractions) over R. The naive matrix multi ..."
Abstract - Cited by 53 (3 self) - Add to MetaCart
Let A and B two n n matrices over a ring R (e.g., the reals or the integers) each containing at most m non-zero elements. We present a new algorithm that multiplies A and B using O(m ) algebraic operations (i.e., multiplications, additions and subtractions) over R. The naive matrix

Group-theoretic algorithms for matrix multiplication

by Henry Cohn, Robert Kleinberg, Balázs Szegedy, Christopher Umans - In Foundations of Computer Science. 46th Annual IEEE Symposium on 23–25 Oct 2005 , 2005
"... We further develop the group-theoretic approach to fast matrix multiplication introduced by Cohn and Umans, and for the first time use it to derive algorithms asymptotically faster than the standard algorithm. We describe several families of wreath product groups that achieve matrix multiplication e ..."
Abstract - Cited by 79 (6 self) - Add to MetaCart
We further develop the group-theoretic approach to fast matrix multiplication introduced by Cohn and Umans, and for the first time use it to derive algorithms asymptotically faster than the standard algorithm. We describe several families of wreath product groups that achieve matrix multiplication

Fast Matrix Multiplication is Stable

by James Demmel, Ioana Dumitriu, Olga Holtz, Robert Kleinberg , 2006
"... We perform forward error analysis for a large class of recursive matrix multiplication algorithms in the spirit of [D. Bini and G. Lotti, Stability of fast algorithms for matrix multiplication, Numer. Math. 36 (1980), 63–72]. As a consequence of our analysis, we show that the exponent of matrix mult ..."
Abstract - Cited by 14 (4 self) - Add to MetaCart
We perform forward error analysis for a large class of recursive matrix multiplication algorithms in the spirit of [D. Bini and G. Lotti, Stability of fast algorithms for matrix multiplication, Numer. Math. 36 (1980), 63–72]. As a consequence of our analysis, we show that the exponent of matrix

Matrix Multiplication on Heterogeneous Platforms

by Olivier Beaumont, Vincent Boudet, Fabrice Rastello, Yves Robert , 2001
"... this paper, we address the issue of implementing matrix multiplication on heterogeneous platforms. We target two different classes of heterogeneous computing resources: heterogeneous networks of workstations and collections of heterogeneous clusters. Intuitively, the problem is to load balance the ..."
Abstract - Cited by 53 (15 self) - Add to MetaCart
this paper, we address the issue of implementing matrix multiplication on heterogeneous platforms. We target two different classes of heterogeneous computing resources: heterogeneous networks of workstations and collections of heterogeneous clusters. Intuitively, the problem is to load balance

Geometry and the complexity of matrix multiplication

by J. M. Landsberg , 2007
"... Abstract. We survey results in algebraic complexity theory, focusing on matrix multiplication. Our goals are (i) to show how open questions in algebraic complexity theory are naturally posed as questions in geometry and representation theory, (ii) to motivate researchers to work on these questions, ..."
Abstract - Cited by 33 (4 self) - Add to MetaCart
Abstract. We survey results in algebraic complexity theory, focusing on matrix multiplication. Our goals are (i) to show how open questions in algebraic complexity theory are naturally posed as questions in geometry and representation theory, (ii) to motivate researchers to work on these questions

Algorithms for Non-negative Matrix Factorization

by Daniel D. Lee, H. Sebastian Seung - In NIPS , 2001
"... Non-negative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. Two different multiplicative algorithms for NMF are analyzed. They differ only slightly in the multiplicative factor used in the update rules. One algorithm can be shown to minim ..."
Abstract - Cited by 1246 (5 self) - Add to MetaCart
Non-negative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. Two different multiplicative algorithms for NMF are analyzed. They differ only slightly in the multiplicative factor used in the update rules. One algorithm can be shown

Matrix Multiplication Performance

by James Canning , 2002
"... This paper presents matrix multiplication performance results for sequential and parallel implementations written in C using Message Passing Interface (MPI) [12] and the parallel array language ZPL [22]. Although matrix multiplication has been addressed by numerious papers in the past, this treatmen ..."
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This paper presents matrix multiplication performance results for sequential and parallel implementations written in C using Message Passing Interface (MPI) [12] and the parallel array language ZPL [22]. Although matrix multiplication has been addressed by numerious papers in the past

Compressed modular matrix multiplication

by Jean-Guillaume Dumas, Laurent Fousse, Bruno Salvy - IN: MILESTONES IN COMPUTER ALGEBRA , 2008
"... We propose to store several integers modulo a small prime into a single machine word. Modular addition is performed by addition and possibly subtraction of a word containing several times the modulo. Modular Multiplication is not directly accessible but modular dot product can be performed by an int ..."
Abstract - Cited by 5 (2 self) - Add to MetaCart
by an integer multiplication by the reverse integer. Modular multiplication by a word containing a single residue is a also possible. Therefore matrix multiplication can be performed on such a compressed storage. We here give bounds on the sizes of primes and matrices for which such a compression is possible

A Data Locality Optimizing Algorithm

by Michael E. Wolf, Monica S. Lam , 1991
"... This paper proposes an algorithm that improves the locality of a loop nest by transforming the code via interchange, reversal, skewing and tiling. The loop transformation algorithm is based on two concepts: a mathematical formulation of reuse and locality, and a loop transformation theory that unifi ..."
Abstract - Cited by 804 (16 self) - Add to MetaCart
that unifies the various transforms as unimodular matrix transformations. The algorithm has been implemented in the SUIF (Stanford University Intermediate Format) compiler, and is successful in optimizing codes such as matrix multiplication, successive over-relaxation (SOR), LU decomposition without pivoting
Results 1 - 10 of 10,728