Related papers: A Systematic Framework for Stable and Cost-Efficie…
A new stabilizer free weak Galerkin (WG) method is introduced and analyzed for the biharmonic equation. Stabilizing/penalty terms are often necessary in the finite element formulations with discontinuous approximations to ensure the…
The Matrix Product method (MPM) has been used in the past to generate variational ansatzs of the ground state (GS) of spin chains and ladders. In this paper we apply the MPM to study the GS of conjugated polymers in the valence bond basis,…
We study the problem of verifiable polynomial evaluation in the user-server and multi-party setups. We propose {INTERPOL}, an information-theoretically verifiable algorithm that allows a user to delegate the evaluation of a polynomial to a…
The averaging method combined with the Lyapunov-Schmidt reduction provides sufficient conditions for the existence of periodic solutions of the following class of perturbative $T$-periodic nonautonomous differential equations…
We present a novel method for approximately equilibrating a matrix $A \in {\bf R}^{m \times n}$ using only multiplication by $A$ and $A^T$. Our method is based on convex optimization and projected stochastic gradient descent, using an…
We use a Monte Carlo method to assemble finite element matrices for polynomial Chaos approximations of elliptic equations with random coefficients. In this approach, all required expectations are approximated by a Monte Carlo method. The…
Matrix completion is widely used in machine learning, engineering control, image processing, and recommendation systems. Currently, a popular algorithm for matrix completion is Singular Value Threshold (SVT). In this algorithm, the singular…
A finitely generated quadratic module or preordering in the real polynomial ring is called stable, if it admits a certain degree bound on the sums of squares in the representation of polynomials. Stability, first defined explicitly by…
Symbolic Mathematical tasks such as integration often require multiple well-defined steps and understanding of sub-tasks to reach a solution. To understand Transformers' abilities in such tasks in a fine-grained manner, we deviate from…
We describe different optimization techniques to perform the assembly of finite element matrices in Matlab and Octave, from the standard approach to recent vectorized ones, without any low level language used. We finally obtain a simple and…
Efficient structural reanalysis for high-rank modification plays an important role in engineering computations which require repeated evaluations of structural responses, such as structural optimization and probabilistic analysis. To…
Complex valued systems with an indefinite matrix term arise in important applications such as for certain time-harmonic partial differential equations such as the Maxwell's equation and for the Helmholtz equation. Complex systems with…
This paper introduces general methodologies for constructing closed-form solutions to linear constant-coefficient partial differential equations (PDEs) with polynomial right-hand sides in two and three spatial dimensions. Polynomial…
It is well known that many problems in interval computation are intractable, which restricts our attempts to solve large problems in reasonable time. This does not mean, however, that all problems are computationally hard. Identifying…
This paper describes a fast algorithm for recovering low-rank matrices from their linear measurements contaminated with Poisson noise: the Poisson noise Maximum Likelihood Singular Value thresholding (PMLSV) algorithm. We propose a convex…
Polygonal finite elements generally do not pass the patch test as a result of quadrature error in the evaluation of weak form integrals. In this work, we examine the consequences of lack of polynomial consistency and show that it can lead…
The matrix factor model has drawn growing attention for its advantage in achieving two-directional dimension reduction simultaneously for matrix-structured observations. In this paper, we propose a simple iterative least squares algorithm…
We consider space-saving versions of several important operations on univariate polynomials, namely power series inversion and division, division with remainder, multi-point evaluation, and interpolation. Now-classical results show that…
We combine the known methods for univariate polynomial root-finding and for computations in the Frobenius matrix algebra with our novel techniques to advance numerical solution of a univariate polynomial equation, and in particular…
The scheme of divided differences is widely used in many approximation and interpolation problems. Computing the Newton coefficients of the interpolating polynomial is the first step of the Bj\"{o}rck and Pereyra algorithm for solving…