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Iterative Closest Point (ICP) is a widely used method for performing scan-matching and registration. Being simple and robust method, it is still computationally expensive and may be challenging to use in real-time applications with limited…

Robotics · Computer Science 2017-09-19 A. L. Pavlov , G. V. Ovchinnikov , D. Yu. Derbyshev , D. Tsetserukou , I. V. Oseledets

We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…

Numerical Analysis · Mathematics 2020-03-31 S. Armstrong , A. Hannukainen , T. Kuusi , J. -C. Mourrat

In this paper, we introduce the new optimal perturbation iteration method based on the perturbation iteration algorithms for the approximate solutions of nonlinear differential equations of many types. The proposed method is illustrated by…

Numerical Analysis · Mathematics 2016-09-21 Sinan Deniz , Necdet Bildik

The aim of this work is to provide fast and accurate approximation schemes for the Monte Carlo pricing of derivatives in LIBOR market models. Standard methods can be applied to solve the stochastic differential equations of the successive…

Computational Finance · Quantitative Finance 2011-07-20 Antonis Papapantoleon , David Skovmand

In this paper we analyse convergence of projected fixed-point iteration on a Riemannian manifold of matrices with fixed rank. As a retraction method we use `projector splitting scheme'. We prove that the projector splitting scheme converges…

Numerical Analysis · Mathematics 2016-04-08 Denis Kolesnikov , Ivan Oseledets

The double-exponential Sinc-collocation method is known as a super-accurate method for solving initial value problems of ordinary differential equations, for which the error decreases almost exponentially as a function of the number of…

Numerical Analysis · Mathematics 2026-04-29 Yusaku Yamamoto , Ken'ichiro Tanaka

In this article, we establish a class of new projected type iteration methods based on matrix spitting for solving the linear complementarity problem. Also, we provide a sufficient condition for the convergence analysis when the system…

Optimization and Control · Mathematics 2023-05-10 Bharat Kumar , Deepmala , A. K. Das

Salkuyeh proposed the Picard-HSS iteration method to solve the absolute value equation (AVE), which is a class of non-differentiable NP-hard problem. To further improve its performance, a nonlinear HSS-like iteration method is proposed.…

Numerical Analysis · Mathematics 2018-01-03 Mu-Zheng Zhu , Ya-E Qi

This paper studies the iteration-complexity of new regularized hybrid proximal extragradient (HPE)-type methods for solving monotone inclusion problems (MIPs). The new (regularized HPE-type) methods essentially consist of instances of the…

Optimization and Control · Mathematics 2015-09-09 Maicon Marques Alves , Renato D. C. Monteiro , Benar F. Svaiter

Motivated by Pryce's structural index reduction method for differential algebraic equations (DAEs), we show the complexity of the fixed-point iteration algorithm and propose a fixed-point iteration method with parameters. It leads to a…

Numerical Analysis · Computer Science 2014-12-22 Juan Tang , Wenyuan Wu , Xiaolin Qin , Yong Feng

Despite the broad use of fixed-point iterations throughout applied mathematics, the optimal convergence rate of general fixed-point problems with nonexpansive nonlinear operators has not been established. This work presents an acceleration…

Optimization and Control · Mathematics 2022-06-28 Jisun Park , Ernest K. Ryu

For a family of stochastic differential equations, we investigate the asymptotic behaviors of its corresponding Picard's iteration, establishing convergence results in terms of relative entropy. Our convergence results complement the…

Probability · Mathematics 2018-10-16 Tsz Hin Ng , Guangyue Han

This paper deals with a modifed iterative projection method for approximating a solution of hierarchical fixed point problems for nearly nonexpansive mappings. Some strong convergence theorems for the proposed method are presented under…

Functional Analysis · Mathematics 2014-03-17 Ibrahim Karahan , Murat Ozdemir

The indefinite least squares (ILS) problem is a generalization of the famous linear least squares problem. It minimizes an indefinite quadratic form with respect to a signature matrix. For this problem, we first propose an impressively…

Numerical Analysis · Mathematics 2022-03-30 Yanjun Zhang , Hanyu Li

In this paper, we consider the coupled N/TH problem, in which the termination criterion for the neutronics iteration adopts an adaptive tolerance with respect to the fuel temperature residual at each Picard iteration. We refer to this…

Numerical Analysis · Mathematics 2023-08-01 Dean Wang , Paul K. Romano

Relying on the classical connection between Backward Stochastic Differential Equations (BSDEs) and non-linear parabolic partial differential equations (PDEs), we propose a new probabilistic learning scheme for solving high-dimensional…

Numerical Analysis · Mathematics 2021-02-25 Jean-François Chassagneux , Junchao Chen , Noufel Frikha , Chao Zhou

We develop a framework for quantitative convergence analysis of Picard iterations of expansive set-valued fixed point mappings. There are two key components of the analysis. The first is a natural generalization of single-valued averaged…

Optimization and Control · Mathematics 2018-09-24 D. Russell Luke , Nguyen H. Thao , Matthew K. Tam

In this paper, we prove the strong convergence theorems for nearly nonexpansive mappings, using the modified Picard-Mann hybrid iteration process in the context of uniformly convex Banach space.

Functional Analysis · Mathematics 2021-01-15 Adrian Ghiura

We introduce a numerical solver for the steady-state Boltzmann equation based on the symmetric Gauss-Seidel (SGS) method. To solve the nonlinear system on each grid cell derived from the SGS method, a fixed-point iteration preconditioned…

Numerical Analysis · Mathematics 2024-09-04 Zhenning Cai , Xiaoyu Dong , Jingwei Hu

In this paper, we introduce a new contraction condition that combines the framework of Singh's extension with the classical Chatterjea contraction. This generalized form, called the Singh-Chatterjea contraction, is defined on the p-th…

Functional Analysis · Mathematics 2025-10-15 Zouaoui Bekri , Nicola Fabiano