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Matrix Multiplication
"... 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
, 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 nonzero 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 ..."
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Cited by 53 (3 self)
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Let A and B two n n matrices over a ring R (e.g., the reals or the integers) each containing at most m nonzero 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
Grouptheoretic algorithms for matrix multiplication
 In Foundations of Computer Science. 46th Annual IEEE Symposium on 23–25 Oct 2005
, 2005
"... We further develop the grouptheoretic 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 ..."
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Cited by 79 (6 self)
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We further develop the grouptheoretic 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
, 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 ..."
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Cited by 14 (4 self)
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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
, 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 ..."
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Cited by 53 (15 self)
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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
, 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, ..."
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Cited by 33 (4 self)
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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 Nonnegative Matrix Factorization
 In NIPS
, 2001
"... Nonnegative 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 ..."
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Cited by 1246 (5 self)
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Nonnegative 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
, 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
 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 ..."
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Cited by 5 (2 self)
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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
, 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 ..."
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Cited by 804 (16 self)
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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 overrelaxation (SOR), LU decomposition without pivoting
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