Related papers: Exploring Commutative Matrix Multiplication Scheme…
In this paper, the canonical polyadic (CP) decomposition of tensors that corresponds to matrix multiplications is studied. Finding the rank of these tensors and computing the decompositions is a fundamental problem of algebraic complexity…
Symmetric nonnegative matrix factorization (NMF), a special but important class of the general NMF, is demonstrated to be useful for data analysis and in particular for various clustering tasks. Unfortunately, designing fast algorithms for…
Fast matrix multiplication algorithms may be useful, provided that their running time is good in practice. Particularly, the leading coefficient of their arithmetic complexity needs to be small. Many sub-cubic algorithms have large leading…
A matrix network is a family of matrices, with relatedness modeled by a weighted graph. We consider the task of completing a partially observed matrix network. We assume a novel sampling scheme where a fraction of matrices might be…
We present a non-commutative algorithm for the multiplication of a 2 x 2 block-matrix by its adjoint, defined by a matrix ring anti-homomorphism. This algorithm uses 5 block products (3 recursive calls and 2 general products)over C or in…
This paper presents new approaches for finding the determinant and inverse of a matrix. The choice of pivot selection is kept arbitrary and can be made according to the users need. So the ill conditioned matrices can be handled easily. The…
In 1969 Strassen showed surprisingly that it is possible to multiply two 2 x 2 matrices using seven multiplications and 18 additions, instead of the naive eight multiplications and four additions. The number of additions was later reduced…
The invariant polytope algorithm was a breakthrough in the joint spectral radius computation, allowing to find the exact value of the joint spectral radius for most matrix families~\cite{GP2013,GP2016}. This algorithm found many…
Almost all known secret sharing schemes work on numbers. Such methods will have difficulty in sharing graphs since the number of graphs increases exponentially with the number of nodes. We propose a secret sharing scheme for graphs where we…
Proposing an effective and flexible matrix to represent a graph is a fundamental challenge that has been explored from multiple perspectives, e.g., filtering in Graph Fourier Transforms. In this work, we develop a novel and general…
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…
We establish basic information about border rank algorithms for the matrix multiplication tensor and other tensors with symmetry. We prove that border rank algorithms for tensors with symmetry (such as matrix multiplication and the…
Lifting exploits symmetries in probabilistic graphical models by using a representative for indistinguishable objects, allowing to carry out query answering more efficiently while maintaining exact answers. In this paper, we investigate how…
Data movement is the dominating factor affecting performance and energy in modern computing systems. Consequently, many algorithms have been developed to minimize the number of I/O operations for common computing patterns. Matrix…
We demonstrate that a series of procedures for increasing the efficiency of transition matrix calculations can be realized by integrating the standard single-spin flip transition matrix method with global cluster flipping techniques. Our…
In this paper we focus on the solution of shifted quasiseparable systems and of more general parameter dependent matrix equations with quasiseparable representations. We propose an efficient algorithm exploiting the invariance of the…
Triangular factorizations are an important tool for solving integral equations and partial differential equations with hierarchical matrices ($\mathcal{H}$-matrices). Experiments show that using an $\mathcal{H}$-matrix LR factorization to…
As the ratio between the rate of computation and rate with which data can be retrieved from various layers of memory continues to deteriorate, a question arises: Will the current best algorithms for computing matrix-matrix multiplication on…
In this paper we introduce a new type of pattern -- a flipping correlation pattern. The flipping patterns are obtained from contrasting the correlations between items at different levels of abstraction. They represent surprising…
A robust algorithm for non-negative matrix factorization (NMF) is presented in this paper with the purpose of dealing with large-scale data, where the separability assumption is satisfied. In particular, we modify the Linear Programming…