Numerical Algorithms

Article	Citations
Halpern-type iterative process for solving split common fixed point and monotone variational inclusion problem between Banach spaces	60
Inertial methods for finding minimum-norm solutions of the split variational inequality problem beyond monotonicity	49
A hybrid three-term conjugate gradient projection method for constrained nonlinear monotone equations with applications	46
Inertial relaxed CQ algorithms for solving a split feasibility problem in Hilbert spaces	33
An algorithm for best rational approximation based on barycentric rational interpolation	31
Analysis of fractal dimension of mixed Riemann-Liouville integral	30
New algorithms and convergence theorems for solving variational inequalities with non-Lipschitz mappings	29
α-robust error analysis of a mixed finite element method for a time-fractional biharmonic equation	28
A two-step modulus-based matrix splitting iteration method for horizontal linear complementarity problems	27
On the numerical structure preservation of nonlinear damped stochastic oscillators	23
Fast second-order time two-mesh mixed finite element method for a nonlinear distributed-order sub-diffusion model	23
The Bakhvalov mesh: a complete finite-difference analysis of two-dimensional singularly perturbed convection-diffusion problems	19
Inertial projection-type methods for solving pseudomonotone variational inequality problems in Hilbert space	19
Newton’s method with fractional derivatives and various iteration processes via visual analysis	19
Dai–Liao extensions of a descent hybrid nonlinear conjugate gradient method with application in signal processing	18
Performance of compact and non-compact structure preserving algorithms to traveling wave solutions modeled by the Kawahara equation	18
A new family of hybrid three-term conjugate gradient methods with applications in image restoration	18
A novel operational vector for solving the general form of distributed order fractional differential equations in the time domain based on the second kind Chebyshev wavelets	18
Local and parallel finite element methods for the coupled Stokes/Darcy model	18
A space-time finite element method for solving linear Riesz space fractional partial differential equations	16
Finite volume approach for fragmentation equation and its mathematical analysis	16
On a fast deterministic block Kaczmarz method for solving large-scale linear systems	16
Temporal second-order difference methods for solving multi-term time fractional mixed diffusion and wave equations	16
A modulus-based formulation for the vertical linear complementarity problem	16
Highly efficient schemes for time-fractional Allen-Cahn equation using extended SAV approach	15

Evolutionary derivation of Runge–Kutta pairs for addressing inhomogeneous linear problems	15
On the preserving of the maximum principle and energy stability of high-order implicit-explicit Runge-Kutta schemes for the space-fractional Allen-Cahn equation	15
$$H^{1}$$-norm error analysis of a robust ADI method on graded mesh for three-dimensional subdiffusion problems	14
Derivation and analysis of computational methods for fractional Laplacian equations with absorbing layers	14
Modulus-based matrix splitting methods for a class of horizontal nonlinear complementarity problems	14
Generalized cross validation for ℓp-ℓq minimization	13
New fourth- and sixth-order classes of iterative methods for solving systems of nonlinear equations and their stability analysis	13
Step-by-step solving schemes based on scalar auxiliary variable and invariant energy quadratization approaches for gradient flows	13
Two second-order and linear numerical schemes for the multi-dimensional nonlinear time-fractional Schrödinger equation	13
Linearly compact scheme for 2D Sobolev equation with Burgers’ type nonlinearity	13
On two-subspace randomized extended Kaczmarz method for solving large linear least-squares problems	13
A new self-adaptive algorithm for solving the split common fixed point problem with multiple output sets in Hilbert spaces	13
On the circumcentered-reflection method for the convex feasibility problem	12
The studies of the linearly modified energy-preserving finite difference methods applied to solve two-dimensional nonlinear coupled wave equations	12
Local and parallel finite element methods based on two-grid discretizations for the nonstationary Navier-Stokes equations	11
Bernstein super fractal interpolation function for countable data systems	11
Error bounds for septic Hermite interpolation and its implementation to study modified Burgers’ equation	11
Supercloseness and postprocessing for linear finite element method on Bakhvalov-type meshes	10
Energy dissipation–preserving time-dependent auxiliary variable method for the phase-field crystal and the Swift–Hohenberg models	10
A first-order inexact primal-dual algorithm for a class of convex-concave saddle point problems	10
New subspace minimization conjugate gradient methods based on regularization model for unconstrained optimization	10
Numerical solution of a class of third-kind Volterra integral equations using Jacobi wavelets	10
A dual symmetric Gauss-Seidel alternating direction method of multipliers for hyperspectral sparse unmixing	10
Two-grid finite element methods for nonlinear time-fractional parabolic equations	9
Global algorithm for a class of multiplicative programs using piecewise linear approximation technique	9
Filtered interpolation for solving Prandtl’s integro-differential equations	9
A two-parameter block triangular preconditioner for double saddle point problem arising from liquid crystal directors modeling	9
A novel alternating-direction implicit spectral Galerkin method for a multi-term time-space fractional diffusion equation in three dimensions	9
Second-order maximum principle preserving Strang’s splitting schemes for anisotropic fractional Allen-Cahn equations	9
A novel high-order numerical scheme and its analysis for the two-dimensional time-fractional reaction-subdiffusion equation	9
Revisiting subgradient extragradient methods for solving variational inequalities	9
On the linear convergence of circumcentered isometry methods	9
A Tseng extragradient method for solving variational inequality problems in Banach spaces	9
Two modified inertial projection algorithms for bilevel pseudomonotone variational inequalities with applications to optimal control problems	9
Scaled three-term derivative-free methods for solving large-scale nonlinear monotone equations	9
On the convergence of Krylov methods with low-rank truncations	9
Convergence of the Nelder-Mead method	9
An implicit-explicit preconditioned direct method for pricing options under regime-switching tempered fractional partial differential models	9
A new computational method based on fractional Lagrange functions to solve multi-term fractional differential equations	9
Alternatives to the EM algorithm for ML estimation of location, scatter matrix, and degree of freedom of the Student t distribution	9
Dimensions of new fractal functions and associated measures	8
The fractional Landweber method for identifying the space source term problem for time-space fractional diffusion equation	8
A nonnegativity preserving algorithm for multilinear systems with nonsingular ${\mathcal M}$-tensors	8
A toolbox of equation-free functions in Matlab/Octave for efficient system level simulation	8
A method of fundamental solutions for heat and wave propagation from lateral Cauchy data	8
A modified inertial three-term conjugate gradient projection method for constrained nonlinear equations with applications in compressed sensing	8
Adaptive Euler methods for stochastic systems with non-globally Lipschitz coefficients	8
Newton method for ℓ0-regularized optimization	8
Two adaptive scaled gradient projection methods for Stiefel manifold constrained optimization	8
Novel energy stable schemes for Swift-Hohenberg model with quadratic-cubic nonlinearity based on the H−1-gradient flow approach	8

Fixing and extending some recent results on the ADMM algorithm	8
On the condition number of Vandermonde matrices with pairs of nearly-colliding nodes	8
Solving decomposable sparse systems	8
Modulus-based synchronous multisplitting iteration methods for large sparse vertical linear complementarity problems	8
Fast Toeplitz eigenvalue computations, joining interpolation-extrapolation matrix-less algorithms and simple-loop theory	7
Local error estimation and step size control in adaptive linear multistep methods	7
Modified Newton integration algorithm with noise suppression for online dynamic nonlinear optimization	7
Inertial accelerated primal-dual methods for linear equality constrained convex optimization problems	7
Convergence analysis of sample average approximation for a class of stochastic nonlinear complementarity problems: from two-stage to multistage	7
PMHSS iteration method and preconditioners for Stokes control PDE-constrained optimization problems	7
Crank-Nicolson-weighted-shifted-Grünwald-difference schemes for space Riesz variable-order fractional diffusion equations	7
On the best achievable quality of limit points of augmented Lagrangian schemes	7
Simple numerical methods of second- and third-order convergence for solving a fully third-order nonlinear boundary value problem	7
Finite element method for singularly perturbed problems with two parameters on a Bakhvalov-type mesh in 2D	7
A simple yet efficient two-step fifth-order weighted-Newton method for nonlinear models	7
A two-grid method for discontinuous Galerkin approximations to nonlinear Sobolev equations	7
Anymatrix: an extensible MATLAB matrix collection	7
High-dimensional sparse Fourier algorithms	7
Analysis of two variants of an inertial projection algorithm for finding the minimum-norm solutions of variational inequality and fixed point problems	7
Completely discrete schemes for 2D Sobolev equations with Burgers’ type nonlinearity	7
Efficient, non-iterative, and decoupled numerical scheme for a new modified binary phase-field surfactant system	7
A fast linearized numerical method for nonlinear time-fractional diffusion equations	7
An upwind DG scheme preserving the maximum principle for the convective Cahn-Hilliard model	7
The conservative characteristic difference method and analysis for solving two-sided space-fractional advection-diffusion equations	6
Continuation Newton methods with the residual trust-region time-stepping scheme for nonlinear equations	6
Unconditionally optimal H1-error estimate of a fast nonuniform L2-1σ scheme for nonlinear subdiffusion equations	6
Accurate and stable numerical method based on the Floater-Hormann interpolation for stochastic Itô-Volterra integral equations	6
A solely time-dependent source reconstruction in a multiterm time-fractional order diffusion equation with non-smooth solutions	6
Adaptive three-term PRP algorithms without gradient Lipschitz continuity condition for nonconvex functions	6
Galerkin finite element method for nonlinear fractional differential equations	6
Crank-Nicolson ADI finite difference/compact difference schemes for the 3D tempered integrodifferential equation associated with Brownian motion	6
Superconvergence analysis of BDF-Galerkin FEM for nonlinear Schrödinger equation	6
Centrality measures for node-weighted networks via line graphs and the matrix exponential	6
Perturbation analysis and condition numbers of mixed least squares-scaled total least squares problem	6
Accurate solutions of structured generalized Kronecker product linear systems	6
Accurate error estimation in CG	6
Projected explicit and implicit Taylor series methods for DAEs	6
A novel numerical scheme for time-fractional Black-Scholes PDE governing European options in mathematical finance	6
A new proximal-like algorithm for solving split variational inclusion problems	6
The strong convergence and stability of explicit approximations for nonlinear stochastic delay differential equations	6
Second-order IMEX scheme for a system of partial integro-differential equations from Asian option pricing under regime-switching jump-diffusion models	6
A priori and a posteriori error analysis for virtual element discretization of elliptic optimal control problem	6
Fully numerical Laplace transform methods	6
Faster randomized block sparse Kaczmarz by averaging	6
A subgradient proximal method for solving a class of monotone multivalued variational inequality problems	6
Stability and convergence analysis of stabilized finite element method for the Kelvin-Voigt viscoelastic fluid flow model	6
A minimum-time obstacle-avoidance path planning algorithm for unmanned aerial vehicles	6
New modulus-based matrix splitting methods for implicit complementarity problem	6
Tensor theta norms and low rank recovery	5
Two-step modulus-based matrix splitting iteration methods for retinex problem	5
A complex structure-preserving algorithm for the full rank decomposition of quaternion matrices and its applications	5
Generalized conformable fractional Newton-type method for solving nonlinear systems	5
An efficient Gauss–Newton algorithm for solving regularized total least squares problems	5
Analysis of an adaptive collocation solution for retarded and neutral delay systems	5
Second derivative backward differentiation formulae for ODEs based on barycentric rational interpolants	5
An adaptive mesh refinement method for indirectly solving optimal control problems	5
Fractional-order Chelyshkov wavelet method for solving variable-order fractional differential equations and an application in variable-order fractional relaxation system	5
A primal-dual splitting algorithm for composite monotone inclusions with minimal lifting	5
Proximal point algorithms based on S-iterative technique for nearly asymptotically quasi-nonexpansive mappings and applications	5
The global convergence of the BFGS method with a modified WWP line search for nonconvex functions	5
Sharp error estimate of a Grünwald–Letnikov scheme for reaction-subdiffusion equations	5
Linearized Krylov subspace Bregman iteration with nonnegativity constraint	5
Enhanced moving least squares method for solving the stochastic fractional Volterra integro-differential equations of Hammerstein type	5
All-at-once method for variable-order time fractional diffusion equations	5
Efficient difference method for time-space fractional diffusion equation with Robin fractional derivative boundary condition	5
Numerical study on Moore-Penrose inverse of tensors via Einstein product	5
RBF–DQ algorithms for elliptic problems in axisymmetric domains	5
On choices of formulations of computing the generalized singular value decomposition of a large matrix pair	5
Mittag–Leffler stability of numerical solutions to time fractional ODEs	5
Global error estimation for explicit general linear methods	5
A dynamic distributed conjugate gradient method for variational inequality problem over the common fixed-point constraints	5
Balanced-norm error estimate of the local discontinuous Galerkin method on layer-adapted meshes for reaction-diffusion problems	5
Improved splitting preconditioner for double saddle point problems arising from liquid crystal director modeling	5
A note on memory-less SR1 and memory-less BFGS methods for large-scale unconstrained optimization	5
Perron communicability and sensitivity of multilayer networks	5
Modified third and fifth order WENO schemes for inviscid compressible flows	5
A robust numerical algorithm on harmonic mesh for parabolic singularly perturbed convection-diffusion problems with time delay	5
A Hessenberg-type algorithm for computing PageRank Problems	5
Tensor extrapolation methods with applications	5
The joint bidiagonalization process with partial reorthogonalization	5

Arbitrarily high-order energy-conserving methods for Poisson problems	5
Weak convergence of Euler scheme for SDEs with low regular drift	5
Total positivity and accurate computations with Gram matrices of Bernstein bases	5
Fast and accurate solvers for weakly singular integral equations	4
BEM-Fading regularization algorithm for Cauchy problems in 2D anisotropic heat conduction	4
A τ-preconditioner for a non-symmetric linear system arising from multi-dimensional Riemann-Liouville fractional diffusion equation	4
Substructured two-grid and multi-grid domain decomposition methods	4
Extrapolated sequential constraint method for variational inequality over the intersection of fixed-point sets	4
Gradient and diagonal Hessian approximations using quadratic interpolation models and aligned regular bases	4
Derivative-free superiorization: principle and algorithm	4
Identification of the source function for a seawater intrusion problem in unconfined aquifer	4
Computing Gaussian quadrature rules with high relative accuracy	4
Generalizing the trapezoidal rule in the complex plane	4
Novel projection methods for solving variational inequality problems and applications	4
A fast solver of Legendre-Laguerre spectral element method for the Camassa-Holm equation	4
Dynamics of Newton-like root finding methods	4
Distribution-dependent SDEs with Hölder continuous drift and α-stable noise	4
A second-order finite difference scheme for the multi-dimensional nonlinear time-fractional Schrödinger equation	4
Mathematical programs with vanishing constraints involving strongly invex functions	4
Local and parallel partition of unity scheme for the mixed Navier-Stokes-Darcy problem	4
Halpern projection methods for solving pseudomonotone multivalued variational inequalities in Hilbert spaces	4
Finite difference formulas in the complex plane	4
Optimal convergence of three iterative methods based on nonconforming finite element discretization for 2D/3D MHD equations	4
Wavelet regularization strategy for the fractional inverse diffusion problem	4
Shift-splitting fixed point iteration method for solving generalized absolute value equations	4
An efficient algorithm for solving piecewise-smooth dynamical systems	4
Analytical and numerical solution techniques for a class of time-fractional integro-partial differential equations	4
Continuous and discrete zeroing dynamics models using JMP function array and design formula for solving time-varying Sylvester-transpose matrix inequality	4
Up to eighth-order maximum-principle-preserving methods for the Allen–Cahn equation	4
A class of new Magnus-type methods for semi-linear non-commutative Itô stochastic differential equations	4
Fast and reliable high-accuracy computation of Gauss–Jacobi quadrature	4
A uniformly accurate exponential wave integrator Fourier pseudo-spectral method with structure-preservation for long-time dynamics of the Dirac equation with small potentials	4
Regularized minimal-norm solution of an overdetermined system of first kind integral equations	4
Systematic implementation of higher order Whitney forms in methods based on discrete exterior calculus	4
Convergence and stability of extended BBVMs for nonlinear delay-differential-algebraic equations with piecewise continuous arguments	4
A null-space approach for large-scale symmetric saddle point systems with a small and non zero (2, 2) block	4
Relationship between time-instant number and precision of ZeaD formulas with proofs	4
Accelerated dynamical approaches for finding the unique positive solution of $\mathcal {K}\mathcal {S}$-tensor equations	4
A mixed virtual element method for the time-fractional fourth-order subdiffusion equation	4
Off-diagonal symmetric nonnegative matrix factorization	4
Numerical treatment of the generalized Love integral equation	4
Computational and theoretical aspects of Romanovski-Bessel polynomials and their applications in spectral approximations	4
Uniform stability for a spatially discrete, subdiffusive Fokker–Planck equation	4
A hybrid inertial and contraction proximal point algorithm for monotone variational inclusions	4
Asynchronous Richardson iterations: theory and practice	4
Globally convergent diagonal Polak–Ribière–Polyak like algorithm for nonlinear equations	4
Minimum residual modified HSS iteration method for a class of complex symmetric linear systems	4
Two-grid finite element method for the dual-permeability-Stokes fluid flow model	4
A sample efficient sparse FFT for arbitrary frequency candidate sets in high dimensions	4
A proximal bundle-based algorithm for nonsmooth constrained multiobjective optimization problems with inexact data	4
Numerical approximations to a singularly perturbed convection-diffusion problem with a discontinuous initial condition	4
Inverse central ordering for the Newton interpolation formula	4
An infeasible interior-point arc-search algorithm for nonlinear constrained optimization	3
An optimal 13-point finite difference scheme for a 2D Helmholtz equation with a perfectly matched layer boundary condition	3
Error estimates of finite difference methods for the Dirac equation in the massless and nonrelativistic regime	3
Conformable vector Traub’s method for solving nonlinear systems	3
Comment on: “A derivative-free iterative method for nonlinear monotone equations with convex constraints”	3
Adjusting the energy of Ball surfaces by modifying unfixed control balls	3
A new linearized maximum principle preserving and energy stability scheme for the space fractional Allen-Cahn equation	3
Numerical solution to a nonlinear McKendrick-Von Foerster equation with diffusion	3
A family of three-term conjugate gradient projection methods with a restart procedure and their relaxed-inertial extensions for the constrained nonlinear pseudo-monotone equations with applications	3
A posteriori error estimations of the Petrov-Galerkin methods for fractional Helmholtz equations	3
Representations of generalized inverses via full-rank QDR decomposition	3
A superconvergent ultra-weak local discontinuous Galerkin method for nonlinear fourth-order boundary-value problems	3
Relaxed Tseng splitting method with double inertial steps for solving monotone inclusions and fixed point problems	3
Analysis of two new parareal algorithms based on the Dirichlet-Neumann/Neumann-Neumann waveform relaxation method for the heat equation	3
Global error estimation for explicit second derivative general linear methods	3
Nonmonotone inexact restoration approach for minimization with orthogonality constraints	3
On equivalence of three-parameter iterative methods for singular symmetric saddle-point problem	3
A highly efficient class of optimal fourth-order methods for solving nonlinear systems	3
A second-order dynamical system for equilibrium problems	3
A linearized high-order Galerkin finite element approach for two-dimensional nonlinear time fractional Klein-Gordon equations	3
On the L$$^{\infty }$$ convergence of a novel fourth-order compact and conservative difference scheme for the generalized Rosenau-KdV-RLW equation	3
Oscillation-preserving Legendre-Galerkin methods for second kind integral equations with highly oscillatory kernels	3
Drift-implicit Euler scheme for sandwiched processes driven by Hölder noises	3
On the backward Euler method for a generalized Ait-Sahalia-type rate model with Poisson jumps	3
A high-order numerical scheme for multidimensional convection-diffusion-reaction equation with time-fractional derivative	3
A meshfree method with a non-overlapping domain decomposition method based on TPS for solving the forward-backward heat equation in two-dimension	3
A new method for solving split equality problems via projection dynamical systems	3
Fitted schemes for Caputo-Hadamard fractional differential equations	3
A low-rank solution method for Riccati equations with indefinite quadratic terms	3
A coarsening algorithm on adaptive red-green-blue refined meshes	3
A variant of PMHSS iteration method for a class of complex symmetric indefinite linear systems	3
A note on stability and fractal dimension of bivariate α-fractal functions	3
Deviation maximization for rank-revealing QR factorizations	3
On the generalized AOR and CG iteration methods for a class of block two-by-two linear systems	3
Three decoupled, second-order accurate, and energy stable schemes for the conserved Allen–Cahn-type block copolymer (BCP) model	3
The generalized quadrature method for a class of highly oscillatory Volterra integral equations	3
Artificial compressibility SAV ensemble algorithms for the incompressible Navier-Stokes equations	3
Efficient quadrature rules for the singularly oscillatory Bessel transforms and their error analysis	3
An hp-version fractional collocation method for Volterra integro-differential equations with weakly singular kernels	3
Interpolation of sparse high-dimensional data	3
Arbitrary high-order linearly implicit energy-preserving algorithms for Hamiltonian PDEs	3
Stability analysis of the method of fundamental solutions with smooth closed pseudo-boundaries for Laplace’s equation: better pseudo-boundaries	3
Fully decoupled, linear, and energy-preserving GSAV difference schemes for the nonlocal coupled sine-Gordon equations in multiple dimensions	3