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In this paper we present an efficient iterative method of order six for the inclusion of the inverse of a given regular matrix. To provide the upper error bound of the outer matrix for the inverse matrix, we combine point and interval…

Numerical Analysis · Mathematics 2014-06-23 Marko D. Petkovic , Miodrag S. Petkovic

For large-scale eigenvalue problems requiring many mutually orthogonal eigenvectors, traditional numerical methods suffer substantial computational and communication costs with limited parallel scalability, primarily due to explicit…

Numerical Analysis · Mathematics 2026-01-12 Shengyue Wang , Aihui Zhou

We develop an iterative refinement method that improves the accuracy of a user-chosen subset of $k$ eigenvectors ($k\ll n$) of an $n\times n$ real symmetric matrix. Using an orthogonal matrix represented in compact WY form, the method…

Numerical Analysis · Mathematics 2026-03-02 Takeshi Terao , Katsuhisa Ozaki , Toshiyuki Imamura , Takeshi Ogita

This paper discusses the explicit inverse of a class of seven-diagonal (near) Toeplitz matrices, which arises in the numerical solutions of nonlinear fourth-order differential equation with a finite difference method. A non-recurrence…

Numerical Analysis · Mathematics 2021-03-19 Bakytzhan Kurmanbek , Yogi Erlangga , Yerlan Amanbek

Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems for partial differential equations. When considering non-stationary problems,…

Numerical Analysis · Computer Science 2016-04-18 Petr N. Vabishchevich

Some variants of the numerical Picard iterations method are presented to solve an IVP for an ordinary differential system. The term numerical emphasizes that a numerical solution is computed. The method consists in replacing the right hand…

Numerical Analysis · Mathematics 2017-08-09 Ernest Scheiber

We point out how Banach Fixed Point Theorem, and the Picard successive approximation methods induced by it, allows us to treat some mathematical methods in Combinatorics. In particular we get, by this way, a proof and an iterative algorithm…

Combinatorics · Mathematics 2018-03-20 Ana Luzon

Pointwise estimates for the gradient of solutions to the $p$-Laplace system with right-hand side in divergence form are established. They enable us to develop a nonlinear counterpart of the classical Calder\'on-Zygmund theory in terms of…

Analysis of PDEs · Mathematics 2015-10-12 Dominic Breit , Andrea Cianchi , Lars Diening , Tuomo Kuusi , Sebastian Schwarzacher

In this work we study the homogenization for eigenvalues of the fractional $p-$Laplace in a bounded domain both with Dirichlet and Neumann conditions. We obtain the convergence of eigenvalues and the explicit order of the convergence rates.

Analysis of PDEs · Mathematics 2015-08-12 Ariel M. Salort

In this paper we consider the iteratively regularized Gauss-Newton method for solving nonlinear ill-posed inverse problems. Under merely Lipschitz condition, we prove that this method together with an a posteriori stopping rule defines an…

Numerical Analysis · Mathematics 2009-11-13 Qinian Jin

Inverse linear programming (LP) has received increasing attention due to its potential to generate efficient optimization formulations that can closely replicate the behavior of a complex system. However, inversely inferred parameters and…

Optimization and Control · Mathematics 2022-02-22 Zahed Shahmoradi , Taewoo Lee

In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…

Numerical Analysis · Mathematics 2021-01-15 Barbara Kaltenbacher , Kha Van Huynh

Efficient solution of the lowest eigenmodes is studied for a family of related eigenvalue problems with common $2\times 2$ block structure. It is assumed that the upper diagonal block varies between different versions while the lower…

Numerical Analysis · Mathematics 2020-06-19 Antti Hannukainen , Jarmo Malinen , Antti Ojalammi

In this article, we describe an implementation of a polynomial system solver to compute the approximate solutions of a 0-dimensional polynomial system with finite precision p-adic arithmetic. We also describe an improvement to an algorithm…

Numerical Analysis · Mathematics 2019-07-09 Avinash Kulkarni

In this paper we deal with a weighted eigenvalue problem for the anisotropic $(p,q)$-Laplacian with Dirichlet boundary conditions. We study the main properties of the first eigenvalue and prove a reverse H\"older type inequality for the…

Analysis of PDEs · Mathematics 2025-02-05 Nunzia Gavitone , Rossano Sannipoli

We introduce a globally convergent relaxed Kacanov scheme for the computation of the discrete minimizer to the $p$-Laplace problem with $2 \leq p < \infty$. The iterative scheme is easy to implement since each iterate results only from the…

Numerical Analysis · Mathematics 2022-10-13 Anna Kh. Balci , Lars Diening , Johannes Storn

The affine inverse eigenvalue problem consists of identifying a real symmetric matrix with a prescribed set of eigenvalues in an affine space. Due to its ubiquity in applications, various instances of the problem have been widely studied in…

Optimization and Control · Mathematics 2019-11-07 Utkan Candogan , Yong Sheng Soh , Venkat Chandrasekaran

We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly non-smooth) regularizer is minimized under the constraint that the solution explains the observations…

Optimization and Control · Mathematics 2012-10-10 Manya V. Afonso , José M. Bioucas-Dias , Mário A. T. Figueiredo

This work tackles an inverse boundary value problem for a $p$-Laplace type partial differential equation parametrized by a smoothening parameter $\tau \geq 0$. The aim is to numerically test reconstructing a conductivity type coefficient in…

Numerical Analysis · Mathematics 2018-03-29 Antti Hannukainen , Nuutti Hyvönen , Lauri Mustonen

It is well known that the usual mixed method for solving the biharmonic eigenvalue problem by decomposing the operator into two Laplacians may generate spurious eigenvalues on non-convex domains. To overcome this difficulty, we adopt a…

Numerical Analysis · Mathematics 2021-07-27 Baiju Zhang , Hengguang Li , Zhimin Zhang