相关论文: A Fast Solver for Tridiagonal Toeplitz Systems wit…

We show constructively that, under certain regularity assumptions, any system of coupled linear differential equations with variable coefficients can be tridiagonalized by a time-dependent Lanczos-like method. The proof we present formally…

In this note we present an algorithm to generate new Schr\" odinger type equations explicitly solvable in terms of orthogonal polynomials or associated special functions.

We present a family of integral equation-based solvers for the linear or semilinear heat equation in complicated moving (or stationary) geometries. This approach has significant advantages over more standard finite element or finite…

We analyze solutions of the Toda system and establish an optimal Moser-Trudinger inequality

In this article we analyze a generalized trapezoidal rule for initial value problems with piecewise smooth right hand side \(F:\R^n\to\R^n\). When applied to such a problem the classical trapezoidal rule suffers from a loss of accuracy if…

The goal of this paper is to provide computational tools able to find a solution of a system of polynomial inequalities. The set of inequalities is reformulated as a system of polynomial equations. Three different methods, two of which…

It is well known that the P3P problem could have 1, 2, 3 and at most 4 positive solutions under different configurations among its 3 control points and the position of the optical center. Since in any real applications, the knowledge on the…

In this study, we develop a new parallel algorithm for solving systems of linear algebraic equations with the same block-tridiagonal matrix but with different right-hand sides. The method is a generalization of the parallel dichotomy…

Cyclic reduction is a method for the solution of (block-)tridiagonal linear systems. In this note we review the method tailored to hermitian positive definite banded linear systems. The reviewed method has the following advantages: It is…

We formally introduce and study Toeplitz operators on the Hardy space of the $n$-dimensional Hartogs triangle. We find a precise relation between these operators and the Toeplitz operators on the Hardy space of the unit polydisc $\mathbb…

We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.

In this paper we study the class of mixed-index time fractional differential equations in which different components of the problem have different time fractional derivatives on the left hand side. We prove a theorem on the solution of the…

We present a new parallel algorithm for solving triangular systems with multiple right hand sides (TRSM). TRSM is used extensively in numerical linear algebra computations, both to solve triangular linear systems of equations as well as to…

The exponential trapezoidal rule is proposed and analyzed for the numerical integration of semilinear integro-differential equations. Although the method is implicit, the numerical solution is easily obtained by standard fixed-point…

We develop a systematic way to solve linear equations involving tensors of arbitrary rank. We start off with the case of a rank $3$ tensor, which appears in many applications, and after finding the condition for a unique solution we derive…

A novel method has been introduced to solve a point inclusion in a polygon problem. The method is applicable to convex as well as non-convex polygons which are not self-intersecting. The introduced method is independent of rounding off…

We propose a novel approach to solve the three-nucleon (3N) Faddeev equation which avoids the complicated singularity pattern going with the moving logarithmic singularities of the standard approach. In this new approach the treatment of…

The Perspective-Three-Point Problem (P3P) is solved by first focusing on determining the directions of the lines through pairs of control points, relative to the camera, rather than the distances from the camera to the control points. The…

We present a fast solver for the 3D high-frequency Helmholtz equation in heterogeneous, constant density, acoustic media. The solver is based on the method of polarized traces, coupled with distributed linear algebra libraries and…

The real symmetric tridiagonal eigenproblem is of outstanding importance in numerical computations; it arises frequently as part of eigensolvers for standard and generalized dense Hermitian eigenproblems that are based on a reduction to…