In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to ...In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.展开更多
A geometric mapping establishes a correspondence between two domains.Since no real object has zero or negative volume,such a mapping is required to be inversion-free.Computing inversion-free mappings is a fundamental ...A geometric mapping establishes a correspondence between two domains.Since no real object has zero or negative volume,such a mapping is required to be inversion-free.Computing inversion-free mappings is a fundamental task in numerous computer graphics and geometric processing applications,such as deformation,texture mapping,mesh generation,and others.This task is usually formulated as a non-convex,nonlinear,constrained optimization problem.Various methods have been developed to solve this optimization problem.As well as being inversion-free,different applications have various further requirements.We expand the discussion in two directions to(i)problems imposing specific constraints and(ii)combinatorial problems.This report provides a systematic overview of inversion-free mapping construction,a detailed discussion of the construction methods,including their strengths and weaknesses,and a description of open problems in this research field.展开更多
基金Supported in part by Natural Science Foundation of Guangxi(2023GXNSFAA026246)in part by the Central Government's Guide to Local Science and Technology Development Fund(GuikeZY23055044)in part by the National Natural Science Foundation of China(62363003)。
文摘In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.
基金supported by the National Natural Science Foundation of China(Nos.61802359 and 61672482)the USTC Research Funds of the Double FirstClass Initiative(No.YD0010002003)。
文摘A geometric mapping establishes a correspondence between two domains.Since no real object has zero or negative volume,such a mapping is required to be inversion-free.Computing inversion-free mappings is a fundamental task in numerous computer graphics and geometric processing applications,such as deformation,texture mapping,mesh generation,and others.This task is usually formulated as a non-convex,nonlinear,constrained optimization problem.Various methods have been developed to solve this optimization problem.As well as being inversion-free,different applications have various further requirements.We expand the discussion in two directions to(i)problems imposing specific constraints and(ii)combinatorial problems.This report provides a systematic overview of inversion-free mapping construction,a detailed discussion of the construction methods,including their strengths and weaknesses,and a description of open problems in this research field.
