High convergence order iterative method for nonlinear system of equations in Banach spaces

Authors: Sharma, Rajni, Deep, Gagan, Bala, Neeru

Source: The Journal of Analysis. 33:989-1018

Subject Terms: Banach spaces, Iterative procedures involving nonlinear operators, efficiency, Numerical solutions to equations with nonlinear operators, local convergence, iterative methods

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Multifidelity Covariance Estimation via Regression on the Manifold of Symmetric Positive Definite Matrices: Multifidelity covariance estimation via regression on the manifold of symmetric positive definite matrices

Authors: Aimee Maurais, Terrence Alsup, Benjamin Peherstorfer, Youssef M. Marzouk

Source: SIAM Journal on Mathematics of Data Science. 7:189-223

Subject Terms: FOS: Computer and information sciences, covariance estimation, Computer Science - Machine Learning, Numerical solutions of ill-posed problems in abstract spaces, regularization, Numerical solutions to equations with nonlinear operators, multifidelity methods, Numerical Analysis (math.NA), estimation on manifolds, Statistics - Computation, Machine Learning (cs.LG), Positive matrices and their generalizations, cones of matrices, Numerical solutions to equations with linear operators, Special polytopes (linear programming, centrally symmetric, etc.), General nonlinear regression, FOS: Mathematics, Mathematics - Numerical Analysis, Riemannian geometry, Mahalanobis distance, Statistics on manifolds, Computation (stat.CO), statistical coupling

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Access URL: http://arxiv.org/abs/2307.12438

The solution of split common fixed point problems for enriched asymptotically nonexpansive mappings in Banach spaces

Authors: Agwu, Imo Kalu, Ali, Faeem, Igbokwe, Donatus Ikechi

Source: The Journal of Analysis. 33:589-617

Subject Terms: Fixed-point theorems, pseudocontractive mapping, Banach space, fixed point, Equations involving nonlinear operators (general), Numerical solutions to equations with nonlinear operators, enriched nonlinear mapping, Lipschitizian and quasi-nonexpansive mappings, Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc, demicontractive mappings, accretive operators

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Iterative algorithms for common fixed points of a countable family of quasi-nonexpansive multivalued mappings in CAT(0) spaces

Authors: Salisu, Sani, Minjibir, Ma'aruf Shehu

Source: Mathematical Sciences. 18:681-692

Subject Terms: strong convergence, CAT(0) space, Fixed-point and coincidence theorems (topological aspects), Numerical solutions to equations with nonlinear operators, \( \triangle \)-convergence, Special maps on metric spaces, demiclosedness-type property, multivalued quasi-nonexpansive mappings, Hausdorff metric, Set-valued maps in general topology

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Access URL: https://zbmath.org/7985536
https://doi.org/10.1007/s40096-024-00524-9

Block‐iterative schemes for the split common fixed point problem and applications: Block-iterative schemes for the split common fixed point problem and applications

Authors: Nguyen Buong, Nguyen Duong Nguyen, Nguyen Thi Quynh Anh

Source: Mathematical Methods in the Applied Sciences. 47:9556-9570

Subject Terms: strong convergence, Landweber-type operator, fixed point, Numerical solutions to equations with nonlinear operators, 0211 other engineering and technologies, Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc, block-iterative scheme, 02 engineering and technology, quasi-nonexpansive mapping, 0101 mathematics, 01 natural sciences, demiclosedness principle, Fixed-point iterations

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Access URL: https://zbmath.org/7883045
https://doi.org/10.1002/mma.10082

Inertial iterative algorithms for common solution of variational inequality and system of variational inclusion problems

Authors: Zhao, Yali, Zhao, Ziru

Source: The Journal of Analysis. 32:2889-2911

Subject Terms: Convex programming, Variational and other types of inequalities involving nonlinear operators (general), Numerical solutions to equations with nonlinear operators, weak convergence, extragradient method

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Access URL: https://zbmath.org/7965063
https://doi.org/10.1007/s41478-024-00766-9

Relaxed Inertial Method for Solving Split Monotone Variational Inclusion Problem with Multiple Output Sets Without Co-coerciveness and Lipschitz Continuity: Relaxed inertial method for solving split monotone variational inclusion problem with multiple output sets without co-coerciveness and Lipschitz continuity

Authors: Alakoya, Timilehin Opeyemi, Mewomo, Oluwatosin Temitope

Source: Acta Mathematica Sinica, English Series. 40:1697-1726

Subject Terms: Iterative procedures involving nonlinear operators, inertial technique, Numerical solutions to equations with nonlinear operators, split inverse problems, non-Lipschitz operators, self-adaptive step sizes, Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming), Numerical methods for variational inequalities and related problems

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Strong Norm Error Bounds for Quasilinear Wave Equations Under Weak CFL-Type Conditions: Strong norm error bounds for quasilinear wave equations under weak CFL-type conditions

Authors: Dörich, Benjamin

Source: Foundations of Computational Mathematics, 25 (1), 303–350

Subject Terms: ddc:510, Numerical solutions to equations with nonlinear operators, nonconforming space discretization, a-priori error bounds, Full discretization, A-priori error bounds, quasilinear wave equation, 01 natural sciences, Nonconforming space discretization, Error bounds for initial value and initial-boundary value problems involving PDEs, Error analysis, full discretization, Wave equation, Isoparametric finite elements, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, 0101 mathematics, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, Quasilinear wave equation, Mathematics, error analysis, isoparametric finite elements

File Description: application/xml; application/pdf

Access URL: https://publikationen.bibliothek.kit.edu/1000168974
https://publikationen.bibliothek.kit.edu/1000168974/152359850
https://doi.org/10.5445/IR/1000168974

Mechanical modeling of arbitrarily perforated orthotropic composites with the numerical manifold method

Authors: D.L. Guo, H.H. Zhang, X.L. Ji, S.Y. Han

Source: Engineering Analysis with Boundary Elements. 158:289-302

Subject Terms: numerical manifold method, holes, Mathematical modeling or simulation for problems pertaining to mechanics of deformable solids, Finite element methods applied to problems in solid mechanics, Numerical solutions to equations with nonlinear operators, mechanical behavior, Composite and mixture properties, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, orthotropic composites, non-conforming discretization

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Access URL: https://zbmath.org/7875814
https://doi.org/10.1016/j.enganabound.2023.11.001

Effective Rates for Iterations Involving Bregman Strongly Nonexpansive Operators: Effective rates for iterations involving Bregman strongly nonexpansive operators

Authors: Nicholas Pischke, Ulrich Kohlenbach

Source: Set-Valued and Variational Analysis. 32

Subject Terms: Iterative procedures involving nonlinear operators, proof mining, Numerical solutions to equations with nonlinear operators, Bregman strongly nonexpansive mappings, Bregman projections, 0211 other engineering and technologies, Legendre functions, maximal monotone operators, 02 engineering and technology, Functionals in proof theory, 0101 mathematics, 01 natural sciences

File Description: application/xml; text

Access URL: https://zbmath.org/7965977
https://doi.org/10.1007/s11228-024-00736-0
https://tuprints.ulb.tu-darmstadt.de/29159/1/11228_2024_Article_736.pdf

Strong convergence algorithm for proximal split feasibility problem

Authors: Ajay Kumar, Balwant Singh Thakur

Source: The Journal of Analysis. 32:137-156

Subject Terms: strong convergence, Fixed-point theorems, Iterative procedures involving nonlinear operators, fixed point problem, Numerical solutions to equations with nonlinear operators, proximal split feasibility problem

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Access URL: https://zbmath.org/7928404
https://doi.org/10.1007/s41478-023-00613-3

An iterative deep Ritz method for monotone elliptic problems

Authors: Tianhao Hu, Bangti Jin, Fengru Wang

Source: Journal of Computational Physics. 527:113791

Subject Terms: deep Ritz method, FOS: Computer and information sciences, Computer Science - Machine Learning, convergence, iterative method, Numerical solutions to equations with nonlinear operators, deep neural network, monotone elliptic problem, FOS: Mathematics, Spectral, collocation and related methods for boundary value problems involving PDEs, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), Machine Learning (cs.LG)

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Access URL: http://arxiv.org/abs/2501.15186
https://zbmath.org/8021092
https://doi.org/10.1016/j.jcp.2025.113791

Iterative methods of order two and three for computing inverse elements in Banach algebra with identity

Authors: Szabó, Zoltán

Source: Publicationes Mathematicae Debrecen. 32:153-164

Subject Terms: Numerical solutions to equations with nonlinear operators, Banach algebra, inverse element, iterative methods, General theory of topological algebras, 0101 mathematics, convergence order, 01 natural sciences

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Access URL: https://zbmath.org/3994932

On an application of the Zincenko method to the approximation of implicit functions

Authors: Argyros, Ioannis K.

Source: Publicationes Mathematicae Debrecen. 40:43-49

Subject Terms: approximate implicit functions in Banach spaces, Iterative procedures involving nonlinear operators, Numerical solutions to equations with nonlinear operators, Zincenko iteration, nonlinear equations, Linear spaces of operators, 0101 mathematics, 01 natural sciences

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Access URL: https://zbmath.org/55009

INERTIAL MANN-KRASNOSELSKII ALGORITHM WITH SELF ADAPTIVE STEPSIZE FOR SPLIT VARIATIONAL INCLUSION PROBLEM AND PARAMONOTONE EQUILIBRIA: Inertial Mann-Krasnoselskii algorithm with self adaptive stepsize for split variational inclusion problem and paramonotone equilibria

Authors: Lateef O. Jolaoso, Akindele A. Mebawondu, Oluwatosin T. Mewomo

Source: Mathematical Modelling and Analysis, Vol 27, Iss 2 (2022)
Mathematical Modelling and Analysis; Vol 27 No 2 (2022); 179–198

Subject Terms: Iterative procedures involving nonlinear operators, split variational inclusion, Numerical solutions to equations with nonlinear operators, QA1-939, self adaptive stepsize, pseudomonotonicity, 0101 mathematics, 01 natural sciences, Mathematics, equilibrium problem, Numerical methods for variational inequalities and related problems

File Description: application/xml; application/pdf

Access URL: https://doaj.org/article/431920407faf410ea4d74b2557331d1a
https://journals.vilniustech.lt/index.php/MMA/article/view/13949

Towards Gaussian Process for operator learning: An uncertainty aware resolution independent operator learning algorithm for computational mechanics: Towards Gaussian process for operator learning: an uncertainty aware resolution independent operator learning algorithm for computational mechanics

Authors: Kumar, Sawan, Nayek, Rajdip, Chakraborty, Souvik

Source: Computer Methods in Applied Mechanics and Engineering. 435:117664

Subject Terms: FOS: Computer and information sciences, Numerical optimization and variational techniques, Initial-boundary value problems for nonlinear higher-order PDEs, operator embedded kernels, Computer Science - Machine Learning, stochastic dual descent, Gaussian process operator, uncertainty quantification, Numerical solutions to equations with nonlinear operators, Flows in porous media, filtration, seepage, neural operators, Machine Learning (stat.ML), Machine Learning (cs.LG), Applications of mathematical programming, Statistics - Machine Learning, Nonparametric regression and quantile regression

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Access URL: http://arxiv.org/abs/2409.10972

A strongly convergent algorithm for solving common variational inclusion with application to image recovery problems

Authors: Raweerote Suparatulatorn, Khuanchanok Chaichana

Source: Applied Numerical Mathematics. 173:239-248

Subject Terms: Iterative procedures involving nonlinear operators, inertial technique, Numerical solutions to equations with nonlinear operators, splitting algorithm, Image processing (compression, reconstruction, etc.) in information and communication theory, common variational inclusion problem, 0101 mathematics, Variational inequalities, image recovery problem, 01 natural sciences, process innovation

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Access URL: https://zbmath.org/7468867
https://doi.org/10.1016/j.apnum.2021.12.006

A Fixed Point Theorem for a Pair of Generalized Nonexpansive Mappings in Uniformly Convex Metric Spaces: A fixed point theorem for a pair of generalized nonexpansive mappings in uniformly convex metric spaces

Authors: Wang, Chao, Fan, Honglei

Source: Journal of Mathematical Study. 55:432-444

Subject Terms: pair of generalized nonexpansive mappings, Fixed-point and coincidence theorems (topological aspects), Krasnoselskii type iterative algorithm, Numerical solutions to equations with nonlinear operators, uniformly convex metric spaces, common fixed point, Special maps on metric spaces, 01 natural sciences, 0104 chemical sciences

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Access URL: https://zbmath.org/7663592
https://doi.org/10.4208/jms.v55n4.22.06

Strong convergence of a self-adaptive inertial Tseng's extragradient method for pseudomonotone variational inequalities and fixed point problems

Authors: Uzor Victor Amarachi, Alakoya Timilehin Opeyemi, Mewomo Oluwatosin Temitope

Source: Open Mathematics, Vol 20, Iss 1, Pp 234-257 (2022)

Subject Terms: 47j25, Numerical solutions to equations with nonlinear operators, tseng's extragradient method, 65j15, 65k15, 0211 other engineering and technologies, 02 engineering and technology, 90c33, adaptive step size, strong convergence, Iterative procedures involving nonlinear operators, fixed point, inertial technique, pseudomonotone, QA1-939, Tseng's extragradient method, demicontractive, Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming), Mathematics, variational inequalities, Numerical methods for variational inequalities and related problems

File Description: application/xml

Access URL: https://zbmath.org/7517553
https://doi.org/10.1515/math-2022-0030
https://doaj.org/article/05561771580a4c78933bd776518d6706

Elliptic Reconstruction and a Posteriori Error Estimates for Fully Discrete Semilinear Parabolic Optimal Control Problems: Elliptic reconstruction and a posteriori error estimates for fully discrete semilinear parabolic optimal control problems

Authors: Manohar, Ram, Sinha, Rajen Kumar

Source: Journal of Computational Mathematics. 40:147-176

Subject Terms: a posteriori error estimates, backward Euler method, 03 medical and health sciences, 0302 clinical medicine, Numerical solutions to equations with nonlinear operators, semilinear parabolic optimal control problem, finite element method, 0502 economics and business, 05 social sciences, elliptic reconstruction, Existence theories for optimal control problems involving partial differential equations, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

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