Related papers: Algorithms for the rational approximation of matri…
Many applications require recovering a matrix of minimal rank within an affine constraint set, with matrix completion a notable special case. Because the problem is NP-hard in general, it is common to replace the matrix rank with the…
We study the problem of ranking with submodular valuations. An instance of this problem consists of a ground set $[m]$, and a collection of $n$ monotone submodular set functions $f^1, \ldots, f^n$, where each $f^i: 2^{[m]} \to R_+$. An…
Maximizing a DR-submodular function subject to a general convex set is an NP-hard problem arising from many applications in combinatorial optimization and machine learning. While it is highly desirable to design efficient approximation…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
Several applied problems are characterized by the need to numerically solve equations with an operator function (matrix function). In particular, in the last decade, mathematical models with a fractional power of an elliptic operator and…
The motivation of this paper is the development of an optimisation method for solving optimisation problems appearing in Chebyshev rational and generalised rational approximation problems, where the approximations are constructed as ratios…
With the increasing application of machine learning (ML) algorithms in embedded systems, there is a rising necessity to design low-cost computer arithmetic for these resource-constrained systems. As a result, emerging models of computation,…
We describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments…
The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…
Low-rank approximation of a matrix function, $f(A)$, is an important task in computational mathematics. Most methods require direct access to $f(A)$, which is often considerably more expensive than accessing $A$. Persson and Kressner (SIMAX…
There are a number of approximation algorithms for NP-hard versions of low rank approximation, such as finding a rank-$k$ matrix $B$ minimizing the sum of absolute values of differences to a given $n$-by-$n$ matrix $A$,…
The traditional view in numerical conformal mapping is that once the boundary correspondence function has been found, the map and its inverse can be evaluated by contour integrals. We propose that it is much simpler, and 10-1000 times…
We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex \emph{proper} algorithms for matrix recovery and support them with rigorous…
In this work we present a low-rank algorithm for computing low-rank approximations of large-scale Lyapunov operator $\varphi$-functions. These computations play a crucial role in implementing of matrix-valued exponential integrators for…
The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context of hierarchical matrices, this operation can be realized by the multiplication of structured block-wise low-rank matrices,…
Low Rank Approximation (LRA) of a matrix is a hot research subject, fundamental for Matrix and Tensor Computations and Big Data Mining and Analysis. Computations with low rank matrices can be performed at sublinear cost -- by using much…
Iterative refinement is particularly popular for numerical solution of linear systems of equations. We extend it to Low Rank Approximation of a matrix (LRA) and observe close link of the resulting algorithm to oversampling techniques,…
Inexact computing also referred to as approximate computing is a style of designing algorithms and computing systems wherein the accuracy of correctness of algorithms executing on them is deliberately traded for significant resource…
The focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of nonlinear equations that arise are solved with Newton's method. There is a trade-off between solving Newton systems…
High-dimensional representations, such as radial basis function networks or tile coding, are common choices for policy evaluation in reinforcement learning. Learning with such high-dimensional representations, however, can be expensive,…