Related papers: A Systematic Framework for Stable and Cost-Efficie…
We consider the problem of secure distributed matrix multiplication (SDMM) in which a user wishes to compute the product of two matrices with the assistance of honest but curious servers. We construct polynomial codes for SDMM by studying a…
A generic method to investigate many-body continuous-variable systems is pedagogically presented. It is based on the notion of matrix product states (so-called MPS) and the algorithms thereof. The method is quite versatile and can be…
Polynomial factorization in conventional sense is an ill-posed problem due to its discontinuity with respect to coefficient perturbations, making it a challenge for numerical computation using empirical data. As a regularization, this paper…
We address combinatorial problems that can be formulated as minimization of a partially separable function of discrete variables (energy minimization in graphical models, weighted constraint satisfaction, pseudo-Boolean optimization, 0-1…
This dissertation presents new results on three different themes all related to matroid polytopes. First we investigate properties of Ehrhart polynomials of matroid polytopes, independence matroid polytopes, and polymatroids. We prove that…
This study presents novel strategies for improving the node-level performance of matrix-free evaluation of continuous and discontinuous Galerkin spatial discretizations on unstructured tetrahedral grids. In our approach the underlying…
We develop a validated numerical procedure for continuation of local stable/unstable manifold patches attached to equilibrium solutions of ordinary differential equations. The procedure has two steps. First we compute an accurate high order…
This paper deals with the polynomial linear system solving with errors (PLSwE) problem. Specifically, we focus on the evaluation-interpolation technique for solving polynomial linear systems and we assume that errors can occur in the…
The algorithm and complexity of approximating the permanent of a matrix is an extensively studied topic. Recently, its connection with quantum supremacy and more specifically BosonSampling draws special attention to the average-case…
Kinetic simulations of collisionless (or weakly collisional) plasmas using the Vlasov equation are often infeasible due to high resolution requirements and the exponential scaling of computational cost with respect to dimension. Recently,…
A well-studied nonlinear extension of the minimum-cost flow problem is to minimize the objective $\sum_{ij\in E} C_{ij}(f_{ij})$ over feasible flows $f$, where on every arc $ij$ of the network, $C_{ij}$ is a convex function. We give a…
Learning the closest matrix product state (MPS) representation of a quantum state enables useful tools for quantum machine learning and analysis of complex quantum systems. In this work, we study the problem of learning MPS in the following…
In this paper, we propose an optimization selection methodology for the ubiquitous sparse matrix-vector multiplication (SpMV) kernel. We propose two models that attempt to identify the major performance bottleneck of the kernel for every…
Polynomial optimization problems are infinite-dimensional, nonconvex, NP-hard, and are often handled in practice with the moment-sums of squares hierarchy of semidefinite programming bounds. We consider problems where the objective function…
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,…
This work is to propose an iterative method of choice to compute a stable subspace of a regular matrix pencil. This approach is to define a sequence of matrix pencils via particular left null spaces. We show that this iteration preserves a…
A matrix framework is presented for the solution of ODEs, including initial-, boundary and inner-value problems. The framework enables the solution of the ODEs for arbitrary nodes. There are four key issues involved in the formulation of…
This paper studies the finite-time stability and stabilization of linear discrete time-varying stochastic systems with multiplicative noise. Firstly, necessary and sufficient conditions for finite-time stability are presented via state…
New iterative methods for solving linear equations are presented that are easy to use, generalize good existing methods, and appear to be faster. The new algorithms mix two kinds of linear recurrence formulas. Older methods have either high…
Techniques for the evaluation of complex polynomials with one and two variables are introduced. Polynomials arise in may areas such as control systems, image and signal processing, coding theory, electrical networks, etc., and their…