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We present a simple randomized polynomial time algorithm to approximate the mixed discriminant of $n$ positive semidefinite $n \times n$ matrices within a factor $2^{O(n)}$. Consequently, the algorithm allows us to approximate in randomized…
The article provides a solution algorithm for the linear programming problem (LPP) with the latter being presented as an antagonistic matrix game so the game's further solution is based on the iterative method. The algorithm is presented as…
A multi-output Gaussian process (GP) is introduced as a model for the joint posterior distribution of the local predictive ability of set of models and/or experts, conditional on a vector of covariates, from historical predictions in the…
We propose a new algorithm for sparse estimation of eigenvectors in generalized eigenvalue problems (GEP). The GEP arises in a number of modern data-analytic situations and statistical methods, including principal component analysis (PCA),…
We present an exact and complete algorithm to isolate the real solutions of a zero-dimensional bivariate polynomial system. The proposed algorithm constitutes an elimination method which improves upon existing approaches in a number of…
The orbit problem is at the heart of symmetry reduction methods for model checking concurrent systems. It asks whether two given configurations in a concurrent system (represented as finite strings over some finite alphabet) are in the same…
Motivated by the problem of matching vertices in two correlated Erd\H{o}s-R\'enyi graphs, we study the problem of matching two correlated Gaussian Wigner matrices. We propose an iterative matching algorithm, which succeeds in polynomial…
An extremely common bottleneck encountered in statistical learning algorithms is inversion of huge covariance matrices, examples being in evaluating Gaussian likelihoods for a large number of data points. We propose general parallel…
We introduce an efficient combination of polyhedral analysis and predicate partitioning. Template polyhedral analysis abstracts numerical variables inside a program by one polyhedron per control location, with a priori fixed directions for…
The periodic Gaussian process (PGP) has been increasingly used to model periodic data due to its high accuracy. Yet, computing the likelihood of PGP has a high computational complexity of $\mathcal{O}\left(n^{3}\right)$ ($n$ is the data…
This paper provides the first meaningful documentation and analysis of an established technique which aims to obtain an approximate solution to linear programming problems prior to applying the primal simplex method. The underlying…
We study the classical problem of minimizing the total weighted completion time on a fixed set of $m$ identical machines working in parallel, the $Pm||\sum w_jC_j$ problem in the standard three field notation for scheduling problems. This…
Packing and covering linear programs (PC-LPs) form an important class of linear programs (LPs) across computer science, operations research, and optimization. In 1993, Luby and Nisan constructed an iterative algorithm for approximately…
The conjugate gradient (CG) method is an efficient iterative method for solving large-scale strongly convex quadratic programming (QP). In this paper we propose some generalized CG (GCG) methods for solving the $\ell_1$-regularized…
In a previous paper, we have shown that any Boolean formula can be encoded as a linear programming problem in the framework of Bayesian probability theory. When applied to NP-complete algorithms, this leads to the fundamental conclusion…
Gaussian processes (GPs) are typically criticised for their unfavourable scaling in both computational and memory requirements. For large datasets, sparse GPs reduce these demands by conditioning on a small set of inducing variables…
Matrix functions are a central topic of linear algebra, and problems requiring their numerical approximation appear increasingly often in scientific computing. We review various limited-memory methods for the approximation of the action of…
In this paper, we tackle the parametric complete multiplicity problem for a univariate polynomial. Our approach to the parametric complete multiplicity problem has a significant difference from the classical method, which relies on repeated…
We address the problem of testing weak optimality of a given solution of a given interval linear program. The problem was recently wrongly stated to be polynomially solvable. We disprove it. We show that the problem is NP-hard in general.…
Since the elimination algorithm of Fourier and Motzkin, many different methods have been developed for solving linear programs. When analyzing the time complexity of LP algorithms, it is typically either assumed that calculations are…