Multidimensional Systems and Signal Processing, ISSN 0923-6082, 7/2019, Volume 30, Issue 3, pp. 1531 - 1544

In this paper, we propose a new primal–dual fixed point algorithm with dynamic stepsize ( $$\hbox {PDFP}^{2}O_{DS_{n}}$$ PDFP 2 O D S n ) for solving convex...

Engineering | Fixed point algorithm | Dynamic stepsize | Signal,Image and Speech Processing | Convex separable minimization | 90C25 | Artificial Intelligence | Proximity operator | 47H09 | Circuits and Systems | Electrical Engineering | COMPUTER SCIENCE, THEORY & METHODS | ENGINEERING, ELECTRICAL & ELECTRONIC | Information science | Algorithms

Engineering | Fixed point algorithm | Dynamic stepsize | Signal,Image and Speech Processing | Convex separable minimization | 90C25 | Artificial Intelligence | Proximity operator | 47H09 | Circuits and Systems | Electrical Engineering | COMPUTER SCIENCE, THEORY & METHODS | ENGINEERING, ELECTRICAL & ELECTRONIC | Information science | Algorithms

Journal Article

Electronic Journal of Linear Algebra, ISSN 1537-9582, 2018, Volume 34, Issue 1, pp. 217 - 230

In this paper, the nonlinear matrix equation X-P + A(T) XA = Q, where p is a positive integer, A is an arbitrary n x n matrix, and Q is a symmetric positive...

Symmetric positive definite | Condition number | Mixed and componentwise | Fixed-point iteration | Matrix equation | MATHEMATICS | FIXED-POINT THEOREMS | ORDERED METRIC-SPACES

Symmetric positive definite | Condition number | Mixed and componentwise | Fixed-point iteration | Matrix equation | MATHEMATICS | FIXED-POINT THEOREMS | ORDERED METRIC-SPACES

Journal Article

IEEE Transactions on Automatic Control, ISSN 0018-9286, 4/2019, pp. 1 - 1

This note develops a distributed algorithm to solve a convex optimization problem with coupled constraints. Both coupled equality and inequality constraints...

smooth convex optimization | Distributed optimization | coupled constraints | fixed stepsize | convergence analysis

smooth convex optimization | Distributed optimization | coupled constraints | fixed stepsize | convergence analysis

Journal Article

Optimization, ISSN 0233-1934, 03/2017, Volume 66, Issue 3, pp. 407 - 415

The split common fixed point problem is an inverse problem that consists in finding an element in a fixed point set such that its image under a bounded linear...

Split common fixed point problem | variable stepsize | projection | strong convergence | FEASIBILITY PROBLEMS | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHMS | OPERATORS | Iterative methods | Algorithms | Theorems | Fixed points (mathematics) | Norms | Linear operators | Standards | Optimization | Convergence

Split common fixed point problem | variable stepsize | projection | strong convergence | FEASIBILITY PROBLEMS | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHMS | OPERATORS | Iterative methods | Algorithms | Theorems | Fixed points (mathematics) | Norms | Linear operators | Standards | Optimization | Convergence

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 04/2018, Volume 332, Issue C, pp. 140 - 158

This study introduces new time-stepping strategies with built-in global error estimators. The new methods propagate the defect along with the numerical...

Ordinary differential equations | Local and global error estimation | Time integration | MATHEMATICS, APPLIED | EXPLICIT PEER METHODS | RUNGE-KUTTA METHODS | PARABOLIC EQUATIONS | FIXED-STEPSIZE METHODS | LINES | INITIAL-VALUE PROBLEMS | ORDER | NUMERICAL-INTEGRATION | CONVERGENCE | NORDSIECK METHODS | Computer science | Algorithms | Analysis | Methods | Differential equations | MATHEMATICS AND COMPUTING

Ordinary differential equations | Local and global error estimation | Time integration | MATHEMATICS, APPLIED | EXPLICIT PEER METHODS | RUNGE-KUTTA METHODS | PARABOLIC EQUATIONS | FIXED-STEPSIZE METHODS | LINES | INITIAL-VALUE PROBLEMS | ORDER | NUMERICAL-INTEGRATION | CONVERGENCE | NORDSIECK METHODS | Computer science | Algorithms | Analysis | Methods | Differential equations | MATHEMATICS AND COMPUTING

Journal Article

Journal of Fixed Point Theory and Applications, ISSN 1661-7738, 12/2017, Volume 19, Issue 4, pp. 2427 - 2436

The split common fixed-point problem is an inverse problem that consists in finding an element in a fixed-point set such that its image under a linear...

Mathematical Methods in Physics | 47J20 | Analysis | Mathematics, general | Mathematics | variable stepsize | projection | 47J25 | 49N45 | 65J15 | Split common fixed-point problem | strong convergence | MATHEMATICS | MATHEMATICS, APPLIED | FEASIBILITY PROBLEM | ALGORITHM | variable step-size | Methods | Algorithms

Mathematical Methods in Physics | 47J20 | Analysis | Mathematics, general | Mathematics | variable stepsize | projection | 47J25 | 49N45 | 65J15 | Split common fixed-point problem | strong convergence | MATHEMATICS | MATHEMATICS, APPLIED | FEASIBILITY PROBLEM | ALGORITHM | variable step-size | Methods | Algorithms

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2010, Volume 216, Issue 5, pp. 1566 - 1570

This paper presents a fixed stepsize Euler scheme for linear impulsive delay differential equations and considers its convergence. We propose a method to take...

Numerical method | Impulsive delay differential equations | Euler scheme | Fixed stepsize | Convergence | EXISTENCE | MATHEMATICS, APPLIED | EXPONENTIAL STABILITY | THEOREMS | Partitions | Computation | Mathematical analysis | Differential equations | Inequalities | Mathematical models | Delay

Numerical method | Impulsive delay differential equations | Euler scheme | Fixed stepsize | Convergence | EXISTENCE | MATHEMATICS, APPLIED | EXPONENTIAL STABILITY | THEOREMS | Partitions | Computation | Mathematical analysis | Differential equations | Inequalities | Mathematical models | Delay

Journal Article

Russian Journal of Numerical Analysis and Mathematical Modelling, ISSN 0927-6467, 12/2008, Volume 23, Issue 6, pp. 567 - 595

This paper deals with asymptotically correct methods to evaluate the local and global errors of Nordsieck formulas applied to ordinary differential equations....

MATHEMATICS, APPLIED | ENGINEERING, MULTIDISCIPLINARY | STABILITY | MULTISTAGE INTEGRATION METHODS | FIXED-STEPSIZE METHODS | FORMULAS | ORDINARY DIFFERENTIAL-EQUATIONS | Research | Error analysis (Mathematics) | Differential equations | Estimation theory

MATHEMATICS, APPLIED | ENGINEERING, MULTIDISCIPLINARY | STABILITY | MULTISTAGE INTEGRATION METHODS | FIXED-STEPSIZE METHODS | FORMULAS | ORDINARY DIFFERENTIAL-EQUATIONS | Research | Error analysis (Mathematics) | Differential equations | Estimation theory

Journal Article

2019 Ural Symposium on Biomedical Engineering, Radioelectronics and Information Technology (USBEREIT), 04/2019, pp. 310 - 312

In this paper we propose the fixed-point implementation of extrapolation ODE solvers with adaptive stepsize. We show the applicability of the given approach...

fixed-point arithmetic | Extrapolation | ordinary differential equations | Conferences | Computational modeling | extrapolation methods | Differential equations | stepsize control | Mathematical model | Finite wordlength effects | chaotic system | Biomedical engineering

fixed-point arithmetic | Extrapolation | ordinary differential equations | Conferences | Computational modeling | extrapolation methods | Differential equations | stepsize control | Mathematical model | Finite wordlength effects | chaotic system | Biomedical engineering

Conference Proceeding

SIAM Journal on Scientific Computing, ISSN 1064-8275, 05/2000, Volume 21, Issue 6, pp. 2275 - 2294

Variable time-stepping algorithms for initial value ordinary differential equations are traditionally designed to solve a problem for a fixed initial condition...

MATHEMATICS, APPLIED | RUNGE-KUTTA SCHEMES | adaptivity | fixed point | long time simulations | stability | stepsize | EQUILIBRIUM STATES

MATHEMATICS, APPLIED | RUNGE-KUTTA SCHEMES | adaptivity | fixed point | long time simulations | stability | stepsize | EQUILIBRIUM STATES

Journal Article

2013 Fourth International Conference on Emerging Intelligent Data and Web Technologies, 09/2013, pp. 734 - 736

In this paper, we propose a conjugate gradient method without line search. The method uses a fixed formula for solving step size, which does not involve any...

conjugate gradient method | fixed formula of stepsize | global convergence | unconstrained optimization

conjugate gradient method | fixed formula of stepsize | global convergence | unconstrained optimization

Conference Proceeding

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 1995, Volume 58, Issue 2, pp. 151 - 169

This work examines the performance of explicit, adaptive, Runge-Kutta based algorithms for solving delay differential equations. The results of Hall (1985) for...

Runge-Kutta method | Delay | Error control | Fixed point | MATHEMATICS, APPLIED | ERROR CONTROL | FIXED POINT | RUNGE-KUTTA METHODS | STABILITY | DELAY | STEPSIZE SELECTION | RUNGE-KUTTA METHOD | SCHEMES

Runge-Kutta method | Delay | Error control | Fixed point | MATHEMATICS, APPLIED | ERROR CONTROL | FIXED POINT | RUNGE-KUTTA METHODS | STABILITY | DELAY | STEPSIZE SELECTION | RUNGE-KUTTA METHOD | SCHEMES

Journal Article

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, ISSN 0253-4142, 08/1996, Volume 106, Issue 3, pp. 289 - 300

The distributed implementation of an algorithm for computing fixed points of an infinity-nonexpansive map is shown to converge to the set of fixed points under...

fixed point computation | MATHEMATICS | distributed algorithm | infinity-nonexpansive map | controlled Markov chains | tapering stepsize

fixed point computation | MATHEMATICS | distributed algorithm | infinity-nonexpansive map | controlled Markov chains | tapering stepsize

Journal Article

Proceedings of the Indian Academy of Sciences - Mathematical Sciences, ISSN 0253-4142, 08/1996, Volume 106, Issue 3, pp. 289 - 300

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2017, Volume 2017, Issue 1, pp. 1 - 10

The split feasibility problem (SFP) is finding a point x ∈ C $x\in C$ such that A x ∈ Q $Ax\in Q$ , where C and Q are nonempty closed convex subsets of Hilbert...

split feasibility problem | 58E35 | minimum-norm solution | regularized CQ algorithm | Analysis | 47H09 | operator norm | Mathematics, general | Mathematics | Applications of Mathematics | 65J15 | strong convergence | MATHEMATICS | MATHEMATICS, APPLIED | PROJECTION ALGORITHM | SETS | ITERATIVE ALGORITHMS | FIXED-POINT PROBLEMS | Theorems | Feasibility | Algorithms | Convergence | Research

split feasibility problem | 58E35 | minimum-norm solution | regularized CQ algorithm | Analysis | 47H09 | operator norm | Mathematics, general | Mathematics | Applications of Mathematics | 65J15 | strong convergence | MATHEMATICS | MATHEMATICS, APPLIED | PROJECTION ALGORITHM | SETS | ITERATIVE ALGORITHMS | FIXED-POINT PROBLEMS | Theorems | Feasibility | Algorithms | Convergence | Research

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 09/2016, Volume 39, Issue 13, pp. 3808 - 3823

In this paper, we consider the split feasibility problem (SFP) in infinite‐dimensional Hilbert spaces and propose some subgradient extragradient‐type...

split feasibility problem | 47H10 | subclass 47H09 | extragradient method | 90C25 | fixed‐point problem | subgradient extragradient method | variational inequality | weak convergence | strong convergence | monotone operator | fixed-point problem | HILBERT-SPACES | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | STRONG-CONVERGENCE THEOREMS | ITERATIVE ALGORITHMS | CQ ALGORITHM | VARIATIONAL-INEQUALITIES | BANACH-SPACES | WEAK-CONVERGENCE | SETS | PSEUDO-CONTRACTIONS | Algorithms | Feasibility | Hilbert space | Fixed points (mathematics) | Mathematical analysis | Mapping | Convergence

split feasibility problem | 47H10 | subclass 47H09 | extragradient method | 90C25 | fixed‐point problem | subgradient extragradient method | variational inequality | weak convergence | strong convergence | monotone operator | fixed-point problem | HILBERT-SPACES | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | STRONG-CONVERGENCE THEOREMS | ITERATIVE ALGORITHMS | CQ ALGORITHM | VARIATIONAL-INEQUALITIES | BANACH-SPACES | WEAK-CONVERGENCE | SETS | PSEUDO-CONTRACTIONS | Algorithms | Feasibility | Hilbert space | Fixed points (mathematics) | Mathematical analysis | Mapping | Convergence

Journal Article

Inverse Problems, ISSN 0266-5611, 08/2012, Volume 28, Issue 8, pp. 85004 - 18

The split feasibility problem (SFP) consists in finding a point in a given closed convex subset of a Hilbert space such that its image under a bounded linear...

VARIATIONAL-INEQUALITIES | PROJECTION | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | APPROXIMATION | RECONSTRUCTION | INVERSE PROBLEMS | ITERATIVE ALGORITHMS | CQ ALGORITHM | PHYSICS, MATHEMATICAL | FIXED-POINTS | STRONG-CONVERGENCE | Algorithms | Mathematical analysis | Norms | Feasibility | Hilbert space | Iterative methods | Linear operators | Convergence

VARIATIONAL-INEQUALITIES | PROJECTION | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | APPROXIMATION | RECONSTRUCTION | INVERSE PROBLEMS | ITERATIVE ALGORITHMS | CQ ALGORITHM | PHYSICS, MATHEMATICAL | FIXED-POINTS | STRONG-CONVERGENCE | Algorithms | Mathematical analysis | Norms | Feasibility | Hilbert space | Iterative methods | Linear operators | Convergence

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 06/2019, Volume 387, pp. 446 - 454

Motivated by the recent paper (Wang and Wu, 2018 ), where the authors proposed a class of functionally-fitted energy-preserving integrators for Poisson...

Quadratic energy preservation | Linear Poisson systems | Exponential integrators | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | RUNGE-KUTTA METHODS | LYAPUNOV FUNCTIONS | 1ST INTEGRALS | HAMILTONIAN-SYSTEMS | PHYSICS, MATHEMATICAL | Rigid structures | Energy | Preservation | Mathematical analysis | Numerical methods | Runge-Kutta method | Integrators | Euler-Lagrange equation | Iterative methods | Matrix methods | Convergence

Quadratic energy preservation | Linear Poisson systems | Exponential integrators | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | RUNGE-KUTTA METHODS | LYAPUNOV FUNCTIONS | 1ST INTEGRALS | HAMILTONIAN-SYSTEMS | PHYSICS, MATHEMATICAL | Rigid structures | Energy | Preservation | Mathematical analysis | Numerical methods | Runge-Kutta method | Integrators | Euler-Lagrange equation | Iterative methods | Matrix methods | Convergence

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2015, Volume 2015, Issue 1, pp. 1 - 14

In this article, we first introduce the concept of T-mapping of a finite family of strictly pseudononspreading mapping , and we show that the fixed point set...

simultaneous iterative method | Mathematical and Computational Biology | fixed point | Analysis | Mathematics, general | feasibility problem | Mathematics | Applications of Mathematics | Topology | strictly pseudononspreading mapping | Differential Geometry | weak convergence | CONVEX FEASIBILITY PROBLEMS | MATHEMATICS, APPLIED | CQ ALGORITHM | HILBERT | SPACE | MATHEMATICS | PROJECTION METHOD | SETS | FIXED-POINT PROBLEMS | Fixed point theory | Usage | Convergence (Mathematics) | Iterative methods (Mathematics) | Mappings (Mathematics) | Operators | Algorithms | Mathematical analysis | Norms | Nonlinearity | Iterative algorithms | Mapping | Iterative methods

simultaneous iterative method | Mathematical and Computational Biology | fixed point | Analysis | Mathematics, general | feasibility problem | Mathematics | Applications of Mathematics | Topology | strictly pseudononspreading mapping | Differential Geometry | weak convergence | CONVEX FEASIBILITY PROBLEMS | MATHEMATICS, APPLIED | CQ ALGORITHM | HILBERT | SPACE | MATHEMATICS | PROJECTION METHOD | SETS | FIXED-POINT PROBLEMS | Fixed point theory | Usage | Convergence (Mathematics) | Iterative methods (Mathematics) | Mappings (Mathematics) | Operators | Algorithms | Mathematical analysis | Norms | Nonlinearity | Iterative algorithms | Mapping | Iterative methods

Journal Article

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Full Text
Inertial extragradient algorithms for strongly pseudomonotone variational inequalities

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 10/2018, Volume 341, pp. 80 - 98

The purpose of this paper is to study and analyze two different kinds of inertial type iterative methods for solving variational inequality problems involving...

Subgradient extragradient method | Projection method | Variational inequality problem | Inertial method | Tseng’s extragradient | Strongly pseudomonotone operator | Tseng's extragradient | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | GRADIENT METHODS | PROXIMAL METHOD | STEP | CONVERGENCE THEOREM | MONOTONE INCLUSION PROBLEMS | EQUILIBRIUM PROBLEMS | FORWARD-BACKWARD ALGORITHM | HILBERT-SPACE | FIXED-POINT PROBLEMS | Analysis | Algorithms

Subgradient extragradient method | Projection method | Variational inequality problem | Inertial method | Tseng’s extragradient | Strongly pseudomonotone operator | Tseng's extragradient | MATHEMATICS, APPLIED | NONEXPANSIVE-MAPPINGS | GRADIENT METHODS | PROXIMAL METHOD | STEP | CONVERGENCE THEOREM | MONOTONE INCLUSION PROBLEMS | EQUILIBRIUM PROBLEMS | FORWARD-BACKWARD ALGORITHM | HILBERT-SPACE | FIXED-POINT PROBLEMS | Analysis | Algorithms

Journal Article

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