Related papers: Regular polynomial interpolation and approximation…
Based on the joint bidiagonalization process of a large matrix pair $\{A,L\}$, we propose and develop an iterative regularization algorithm for the large scale linear discrete ill-posed problems in general-form regularization: $\min\|Lx\| \…
In this paper, we propose a new trigonometric interpolation algorithm and establish relevant convergent properties. The method adjusts an existing trigonometric interpolation algorithm such that it can better leverage Fast Fourier Transform…
The recently introduced polynomial time integration framework proposes a novel way to construct time integrators for solving systems of first-order ordinary differential equation by using interpolating polynomials in the complex time plane.…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using…
This paper investigates analytical approximate solutions for a system of multipantograph delay differential equations using the residual power series method (RPSM), which obtains a Taylor expansion of the solutions and produces the exact…
The paper proposes a general quasi-interpolation scheme for high-dimensional function approximation. To facilitate error analysis, we view our quasi-interpolation as a two-step procedure. In the first step, we approximate a target function…
We are interested in numerically approximating the solution ${\bf U}(t)$ of the large dimensional semilinear matrix differential equation $\dot{\bf U}(t) = { \bf A}{\bf U}(t) + {\bf U}(t){ \bf B} + {\cal F}({\bf U},t)$, with appropriate…
We describe a recursive algorithm that decomposes an algebraic set into locally closed equidimensional sets, i.e. sets which each have irreducible components of the same dimension. At the core of this algorithm, we combine ideas from the…
Flux reconstruction provides a framework for solving partial differential equations in which functions are discontinuously approximated within elements. Typically, this is done by using polynomials. Here, the use of radial basis functions…
Motivated by polynomial approximations of differential forms, we study analytical and numerical properties of a polynomial interpolation problem that relies on function averages over interval segments. The usage of segment data gives rise…
In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…
This is a sequel of our previous paper where we described an algorithm to find a solution of differential equations for master integrals in the form of an $\epsilon$-expansion series with numerical coefficients. The algorithm is based on…
In this paper, we study a generalized finite element method for solving second-order elliptic partial differential equations with rough coefficients. The method uses local approximation spaces computed by solving eigenvalue problems on…
Inverse Vandermonde matrix calculation is a long-standing problem to solve nonsingular linear system $Vc=b$ where the rows of a square matrix $V$ are constructed by progression of the power polynomials. It has many applications in…
We give explicit formulas as well as a quadratic time algorithm to solve (so called) generalized Vandermonde's systems of p linear equations and n variables. It allows in particular to find all (so called Lagrange's) interpolation polynoms…
Matrices resulting from the discretization of a kernel function, e.g., in the context of integral equations or sampling probability distributions, can frequently be approximated by interpolation. In order to improve the efficiency, a…
Solving Linear Ordinary Differential Equations (ODEs) plays an important role in many applications. There are various numerical methods and solvers to obtain approximate solutions. However, few work about global error estimation can be…
Interpolation and smoothing using cubic and generalized splines are fundamental tools in data analysis and statistical modeling. Recently, fast computational algorithms were developed for natural $L$-splines of order four, which arise as…
We study how to solve semidefinite programming relaxations for large scale polynomial optimization. When interior-point methods are used, typically only small or moderately large problems could be solved. This paper studies regularization…