Related papers: A New Algorithm for Computing the Actions of Trigo…
The LMS algorithm is one of the most successful adaptive filtering algorithms. It uses the instantaneous value of the square of the error signal as an estimate of the mean-square error (MSE). The LMS algorithm changes (adapts) the filter…
We present a novel recursive algorithm for reducing a symmetric matrix to a triangular factorization which reveals the rank profile matrix. That is, the algorithm computes a factorization $\mathbf{P}^T\mathbf{A}\mathbf{P} =…
Motivated by the problems of computing sample covariance matrices, and of transforming a collection of vectors to a basis where they are sparse, we present a simple algorithm that computes an approximation of the product of two n-by-n real…
This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a…
This paper presents a quadratic formula-based nonlinear representation for a given single-variable function f(x), $-1 \leq x \leq 1$. First, we construct the explicit polynomial coefficient functions a(x), b(x), and c(x) using a…
In this paper, we present novel deterministic algorithms for multiplying two $n \times n$ matrices approximately. Given two matrices $A,B$ we return a matrix $C'$ which is an \emph{approximation} to $C = AB$. We consider the notion of…
An algorithm for computing an analytic function of a matrix $A$ is described. The algorithm is intended for the case where $A$ has some close eigenvalues, and clusters (subsets) of close eigenvalues are separated from each other. This…
A novel parallel algorithm for matrix multiplication is presented. The hyper-systolic algorithm makes use of a one-dimensional processor abstraction. The procedure can be implemented on all types of parallel systems. It can handle…
We consider the task of approximating a matrix function $f(A)$, where $A$ is a matrix in which only a relatively small number of (not necessarily consecutive) sub- and superdiagonals contain nonzero entries. Approximating $f$ by a…
A new Las Vegas algorithm is presented for the composition of two polynomials modulo a third one, over an arbitrary field. When the degrees of these polynomials are bounded by $n$, the algorithm uses $O(n^{1.43})$ field operations, breaking…
Algorithms and implementations for computing the sign function of a triangular matrix are fundamental building blocks in algorithms for computing the sign of arbitrary square real or complex matrices. We present novel recursive and cache…
We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low dimensional variable interactions. Compactly supported periodic Chui-Wang wavelets are used for the tensorized hyperbolic wavelet…
We design new polynomials for representing threshold functions in three different regimes: probabilistic polynomials of low degree, which need far less randomness than previous constructions, polynomial threshold functions (PTFs) with…
Hyperbolic networks have shown prominent improvements over their Euclidean counterparts in several areas involving hierarchical datasets in various domains such as computer vision, graph analysis, and natural language processing. However,…
We propose a matrix-free algorithm for evaluating linear combinations of $\varphi$-function actions, $w_i := \sum_{j=0}^{p} \alpha_i^{\,j}\,\varphi_j(t_i A)v_j$ for $i=1\colon r$, arising in exponential integrators. The method combines the…
In this paper a two-sided, parallel Kogbetliantz-type algorithm for the hyperbolic singular value decomposition (HSVD) of real and complex square matrices is developed, with a single assumption that the input matrix, of order $n$, admits…
We propose a new polynomial-time algorithm for linear programming. We further extend the ideas used in this new linear programming algorithm for nonlinear programming problems. The new algorithm is based on the idea of treating the…
We present new results on Boolean matrix factorization and a new algorithm based on these results. The results emphasize the significance of factorizations that provide from-below approximations of the input matrix. While the previously…
A novel algorithm for computing the action of a matrix exponential over a vector is proposed. The algorithm is based on a multilevel Monte Carlo method, and the vector solution is computed probabilistically generating suitable random paths…
The Active Subspace (AS) method is a widely used technique for identifying the most influential directions in high-dimensional input spaces that affect the output of a computational model. The standard AS algorithm requires a sufficient…