Numerical Algorithms

Article	Citations
Halpern-type iterative process for solving split common fixed point and monotone variational inclusion problem between Banach spaces	59
Inertial methods for finding minimum-norm solutions of the split variational inequality problem beyond monotonicity	45
A hybrid three-term conjugate gradient projection method for constrained nonlinear monotone equations with applications	37
Inertial relaxed CQ algorithms for solving a split feasibility problem in Hilbert spaces	31
New algorithms and convergence theorems for solving variational inequalities with non-Lipschitz mappings	28
An algorithm for best rational approximation based on barycentric rational interpolation	27
Descent Perry conjugate gradient methods for systems of monotone nonlinear equations	25
A two-step modulus-based matrix splitting iteration method for horizontal linear complementarity problems	25
α-robust error analysis of a mixed finite element method for a time-fractional biharmonic equation	23
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
Analysis of fractal dimension of mixed Riemann-Liouville integral	21
The Bakhvalov mesh: a complete finite-difference analysis of two-dimensional singularly perturbed convection-diffusion problems	19
Newton’s method with fractional derivatives and various iteration processes via visual analysis	19
Inertial projection-type methods for solving pseudomonotone variational inequality problems in Hilbert space	18
Local and parallel finite element methods for the coupled Stokes/Darcy model	18
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 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	17
A second-order fast compact scheme with unequal time-steps for subdiffusion problems	17
A space-time finite element method for solving linear Riesz space fractional partial differential equations	16
Golub–Kahan bidiagonalization for ill-conditioned tensor equations with applications	15
Finite volume approach for fragmentation equation and its mathematical analysis	15
Evolutionary derivation of Runge–Kutta pairs for addressing inhomogeneous linear problems	14
A new family of hybrid three-term conjugate gradient methods with applications in image restoration	14

Temporal second-order difference methods for solving multi-term time fractional mixed diffusion and wave equations	14
On block Gaussian sketching for the Kaczmarz method	13
Highly efficient schemes for time-fractional Allen-Cahn equation using extended SAV approach	13
A new self-adaptive algorithm for solving the split common fixed point problem with multiple output sets in Hilbert spaces	13
Modulus-based matrix splitting methods for a class of horizontal nonlinear complementarity problems	13
Two second-order and linear numerical schemes for the multi-dimensional nonlinear time-fractional Schrödinger equation	13
New fourth- and sixth-order classes of iterative methods for solving systems of nonlinear equations and their stability analysis	13
A fast temporal second-order compact ADI difference scheme for the 2D multi-term fractional wave equation	13
Generalized cross validation for ℓp-ℓq minimization	13
Derivation and analysis of computational methods for fractional Laplacian equations with absorbing layers	13
On a fast deterministic block Kaczmarz method for solving large-scale linear systems	12
Convergence analysis of the product integration method for solving the fourth kind integral equations with weakly singular kernels	12
Two energy-conserving and compact finite difference schemes for two-dimensional Schrödinger-Boussinesq equations	12
On two-subspace randomized extended Kaczmarz method for solving large linear least-squares problems	12
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	12
Step-by-step solving schemes based on scalar auxiliary variable and invariant energy quadratization approaches for gradient flows	12
$$H^{1}$$-norm error analysis of a robust ADI method on graded mesh for three-dimensional subdiffusion problems	12
Linearly compact scheme for 2D Sobolev equation with Burgers’ type nonlinearity	12
A modulus-based formulation for the vertical linear complementarity problem	12
The studies of the linearly modified energy-preserving finite difference methods applied to solve two-dimensional nonlinear coupled wave equations	11
On the circumcentered-reflection method for the convex feasibility problem	11
Oscillation-preserving algorithms for efficiently solving highly oscillatory second-order ODEs	11
Local and parallel finite element methods based on two-grid discretizations for the nonstationary Navier-Stokes equations	11
Error bounds for septic Hermite interpolation and its implementation to study modified Burgers’ equation	11
A new strong convergence for solving split variational inclusion problems	10
Jacobi spectral approximation for boundary value problems of nonlinear fractional pantograph differential equations	10
Numerical solution of a class of third-kind Volterra integral equations using Jacobi wavelets	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	9
Global algorithm for a class of multiplicative programs using piecewise linear approximation technique	9
Near-optimal tension parameters in convexity preserving interpolation by generalized cubic splines	9
A dual symmetric Gauss-Seidel alternating direction method of multipliers for hyperspectral sparse unmixing	9
A two-parameter block triangular preconditioner for double saddle point problem arising from liquid crystal directors modeling	9
On the linear convergence of circumcentered isometry methods	9
Alternatives to the EM algorithm for ML estimation of location, scatter matrix, and degree of freedom of the Student t distribution	9
Revisiting subgradient extragradient methods for solving variational inequalities	9
An implicit-explicit preconditioned direct method for pricing options under regime-switching tempered fractional partial differential models	9
Two modified inertial projection algorithms for bilevel pseudomonotone variational inequalities with applications to optimal control problems	8
On the condition number of Vandermonde matrices with pairs of nearly-colliding nodes	8
New subspace minimization conjugate gradient methods based on regularization model for unconstrained optimization	8
Convergence of the Nelder-Mead method	8
Fixing and extending some recent results on the ADMM algorithm	8
Supercloseness and postprocessing for linear finite element method on Bakhvalov-type meshes	8
A nonnegativity preserving algorithm for multilinear systems with nonsingular ${\mathcal M}$-tensors	8
A Tseng extragradient method for solving variational inequality problems in Banach spaces	8
Novel energy stable schemes for Swift-Hohenberg model with quadratic-cubic nonlinearity based on the H−1-gradient flow approach	8
A novel alternating-direction implicit spectral Galerkin method for a multi-term time-space fractional diffusion equation in three dimensions	8
A toolbox of equation-free functions in Matlab/Octave for efficient system level simulation	8
Solving decomposable sparse systems	8
A method of fundamental solutions for heat and wave propagation from lateral Cauchy data	8

Crank-Nicolson-weighted-shifted-Grünwald-difference schemes for space Riesz variable-order fractional diffusion equations	7
Analysis of two variants of an inertial projection algorithm for finding the minimum-norm solutions of variational inequality and fixed point problems	7
Second-order maximum principle preserving Strang’s splitting schemes for anisotropic fractional Allen-Cahn equations	7
A novel high-order numerical scheme and its analysis for the two-dimensional time-fractional reaction-subdiffusion equation	7
Two adaptive scaled gradient projection methods for Stiefel manifold constrained optimization	7
Block collocation boundary value solutions of the first-kind Volterra integral equations	7
High-dimensional sparse Fourier algorithms	7
Local error estimation and step size control in adaptive linear multistep methods	7
Adaptive Euler methods for stochastic systems with non-globally Lipschitz coefficients	7
On the convergence of Krylov methods with low-rank truncations	7
Convergence analysis of sample average approximation for a class of stochastic nonlinear complementarity problems: from two-stage to multistage	7
Filtered interpolation for solving Prandtl’s integro-differential equations	7
Anymatrix: an extensible MATLAB matrix collection	7
A new computational method based on fractional Lagrange functions to solve multi-term fractional differential equations	7
The fractional Landweber method for identifying the space source term problem for time-space fractional diffusion equation	7
Two-grid finite element methods for nonlinear time-fractional parabolic equations	7
Newton method for ℓ0-regularized optimization	7
Inertial accelerated primal-dual methods for linear equality constrained convex optimization problems	7
A two-grid method for discontinuous Galerkin approximations to nonlinear Sobolev equations	7
Bernstein super fractal interpolation function for countable data systems	7
Convergence analysis on matrix splitting iteration algorithm for semidefinite linear complementarity problems	6
A simple yet efficient two-step fifth-order weighted-Newton method for nonlinear models	6
A new proximal-like algorithm for solving split variational inclusion problems	6
Centrality measures for node-weighted networks via line graphs and the matrix exponential	6
A multiresolution algorithm to generate images of generalized fuzzy fractal attractors	6
Fully numerical Laplace transform methods	6
Scaled three-term derivative-free methods for solving large-scale nonlinear monotone equations	6
Modified Newton integration algorithm with noise suppression for online dynamic nonlinear optimization	6
Numerical correction of finite difference solution for two-dimensional space-fractional diffusion equations with boundary singularity	6
Completely discrete schemes for 2D Sobolev equations with Burgers’ type nonlinearity	6
Efficient, non-iterative, and decoupled numerical scheme for a new modified binary phase-field surfactant system	6
Dimensions of new fractal functions and associated measures	6
Fast Toeplitz eigenvalue computations, joining interpolation-extrapolation matrix-less algorithms and simple-loop theory	6
A solely time-dependent source reconstruction in a multiterm time-fractional order diffusion equation with non-smooth solutions	6
Finite element method for singularly perturbed problems with two parameters on a Bakhvalov-type mesh in 2D	6
Stability and convergence analysis of stabilized finite element method for the Kelvin-Voigt viscoelastic fluid flow model	6
A subgradient proximal method for solving a class of monotone multivalued variational inequality problems	6
A fast linearized numerical method for nonlinear time-fractional diffusion equations	6
An upwind DG scheme preserving the maximum principle for the convective Cahn-Hilliard model	6
On the best achievable quality of limit points of augmented Lagrangian schemes	6
Accurate solutions of structured generalized Kronecker product linear systems	6
Faster randomized block sparse Kaczmarz by averaging	6
Modified third and fifth order WENO schemes for inviscid compressible flows	5
Numerical study on Moore-Penrose inverse of tensors via Einstein product	5
Tensor extrapolation methods with applications	5
Mittag–Leffler stability of numerical solutions to time fractional ODEs	5
Proximal point algorithms based on S-iterative technique for nearly asymptotically quasi-nonexpansive mappings and applications	5
Crank-Nicolson ADI finite difference/compact difference schemes for the 3D tempered integrodifferential equation associated with Brownian motion	5
Two-step modulus-based matrix splitting iteration methods for retinex problem	5
The strong convergence and stability of explicit approximations for nonlinear stochastic delay differential equations	5
Linearized Krylov subspace Bregman iteration with nonnegativity constraint	5
An iterated quasi-interpolation approach for derivative approximation	5
All-at-once method for variable-order time fractional diffusion equations	5
Unconditionally optimal H1-error estimate of a fast nonuniform L2-1σ scheme for nonlinear subdiffusion equations	5
Simple numerical methods of second- and third-order convergence for solving a fully third-order nonlinear boundary value problem	5
An adaptive mesh refinement method for indirectly solving optimal control problems	5
On choices of formulations of computing the generalized singular value decomposition of a large matrix pair	5
Sharp error estimate of a Grünwald–Letnikov scheme for reaction-subdiffusion equations	5
Tensor theta norms and low rank recovery	5
The conservative characteristic difference method and analysis for solving two-sided space-fractional advection-diffusion equations	5
Second-order IMEX scheme for a system of partial integro-differential equations from Asian option pricing under regime-switching jump-diffusion models	5
Improved splitting preconditioner for double saddle point problems arising from liquid crystal director modeling	5
Continuation Newton methods with the residual trust-region time-stepping scheme for nonlinear equations	5
Perturbation analysis and condition numbers of mixed least squares-scaled total least squares problem	5
Perron communicability and sensitivity of multilayer networks	5
Analysis of an adaptive collocation solution for retarded and neutral delay systems	5
A Hessenberg-type algorithm for computing PageRank Problems	5
The joint bidiagonalization process with partial reorthogonalization	5
Projected explicit and implicit Taylor series methods for DAEs	5
New modulus-based matrix splitting methods for implicit complementarity problem	5
A minimum-time obstacle-avoidance path planning algorithm for unmanned aerial vehicles	5
A note on memory-less SR1 and memory-less BFGS methods for large-scale unconstrained optimization	5
Superconvergence analysis of BDF-Galerkin FEM for nonlinear Schrödinger equation	5
PMHSS iteration method and preconditioners for Stokes control PDE-constrained optimization problems	5
A modified inertial three-term conjugate gradient projection method for constrained nonlinear equations with applications in compressed sensing	5
RMVPIA: a new algorithm for computing the Lagrange multivariate polynomial interpolation	5
A primal-dual splitting algorithm for composite monotone inclusions with minimal lifting	4
Convergence and dynamics of improved Chebyshev-Secant-type methods for non differentiable operators	4
Galerkin finite element method for nonlinear fractional differential equations	4
BEM-Fading regularization algorithm for Cauchy problems in 2D anisotropic heat conduction	4

Up to eighth-order maximum-principle-preserving methods for the Allen–Cahn equation	4
Halpern projection methods for solving pseudomonotone multivalued variational inequalities in Hilbert spaces	4
Substructured two-grid and multi-grid domain decomposition methods	4
A null-space approach for large-scale symmetric saddle point systems with a small and non zero (2, 2) block	4
Superconvergence in H1-norm of a difference finite element method for the heat equation in a 3D spatial domain with almost-uniform mesh	4
Balanced-norm error estimate of the local discontinuous Galerkin method on layer-adapted meshes for reaction-diffusion problems	4
Local and parallel partition of unity scheme for the mixed Navier-Stokes-Darcy problem	4
Continuous and discrete zeroing dynamics models using JMP function array and design formula for solving time-varying Sylvester-transpose matrix inequality	4
Globally convergent diagonal Polak–Ribière–Polyak like algorithm for nonlinear equations	4
Derivative-free superiorization: principle and algorithm	4
Accurate error estimation in CG	4
A sample efficient sparse FFT for arbitrary frequency candidate sets in high dimensions	4
A fast solver of Legendre-Laguerre spectral element method for the Camassa-Holm equation	4
Total positivity and accurate computations with Gram matrices of Bernstein bases	4
Shift-splitting fixed point iteration method for solving generalized absolute value equations	4
A τ-preconditioner for a non-symmetric linear system arising from multi-dimensional Riemann-Liouville fractional diffusion equation	4
Weak convergence of Euler scheme for SDEs with low regular drift	4
Accelerated dynamical approaches for finding the unique positive solution of $\mathcal {K}\mathcal {S}$-tensor equations	4
An efficient Gauss–Newton algorithm for solving regularized total least squares problems	4
Generalizing the trapezoidal rule in the complex plane	4
Wavelet regularization strategy for the fractional inverse diffusion problem	4
Modulus-based synchronous multisplitting iteration methods for large sparse vertical linear complementarity problems	4
Extrapolated sequential constraint method for variational inequality over the intersection of fixed-point sets	4
Systematic implementation of higher order Whitney forms in methods based on discrete exterior calculus	4
A hybrid inertial and contraction proximal point algorithm for monotone variational inclusions	4
A class of new Magnus-type methods for semi-linear non-commutative Itô stochastic differential equations	4
Adaptive three-term PRP algorithms without gradient Lipschitz continuity condition for nonconvex functions	4
RBF–DQ algorithms for elliptic problems in axisymmetric domains	4
Minimum residual modified HSS iteration method for a class of complex symmetric linear systems	4
Arbitrarily high-order energy-conserving methods for Poisson problems	4
On the eigenvalues of spectral gaps of matrix-valued Schrödinger operators	4
Optimal convergence of three iterative methods based on nonconforming finite element discretization for 2D/3D MHD equations	4
Identification of the source function for a seawater intrusion problem in unconfined aquifer	4
A priori and a posteriori error analysis for virtual element discretization of elliptic optimal control problem	4
A mixed virtual element method for the time-fractional fourth-order subdiffusion equation	4
The global convergence of the BFGS method with a modified WWP line search for nonconvex functions	4
Off-diagonal symmetric nonnegative matrix factorization	4
A second-order finite difference scheme for the multi-dimensional nonlinear time-fractional Schrödinger equation	4
An efficient algorithm for solving piecewise-smooth dynamical systems	4
Inverse central ordering for the Newton interpolation formula	4
Efficient difference method for time-space fractional diffusion equation with Robin fractional derivative boundary condition	4
A robust numerical algorithm on harmonic mesh for parabolic singularly perturbed convection-diffusion problems with time delay	4
Regularized minimal-norm solution of an overdetermined system of first kind integral equations	4
Choice of the parameters in a primal-dual algorithm for Bregman iterated variational regularization	4
Fractional-order Chelyshkov wavelet method for solving variable-order fractional differential equations and an application in variable-order fractional relaxation system	4
Numerical treatment of the generalized Love integral equation	4
Distribution-dependent SDEs with Hölder continuous drift and α-stable noise	3
Explicit pseudo two-step exponential Runge–Kutta methods for the numerical integration of first-order differential equations	3
Efficient quadrature rules for the singularly oscillatory Bessel transforms and their error analysis	3
Nonmonotone inexact restoration approach for minimization with orthogonality constraints	3
Asynchronous Richardson iterations: theory and practice	3
Highly scalable hybrid domain decomposition method for the solution of huge scalar variational inequalities	3
A linearized high-order Galerkin finite element approach for two-dimensional nonlinear time fractional Klein-Gordon equations	3
Structured backward error analysis for a class of block three-by-three saddle point problems	3
Error estimates of finite difference methods for the Dirac equation in the massless and nonrelativistic regime	3
Computing Gaussian quadrature rules with high relative accuracy	3
Dynamics of Newton-like root finding methods	3
A numerical method for the approximation of stable and unstable manifolds of microscopic simulators	3
Stability analysis of the method of fundamental solutions with smooth closed pseudo-boundaries for Laplace’s equation: better pseudo-boundaries	3
Accurate and stable numerical method based on the Floater-Hormann interpolation for stochastic Itô-Volterra integral equations	3
A new method for solving split equality problems via projection dynamical systems	3
Novel projection methods for solving variational inequality problems and applications	3
A low-rank solution method for Riccati equations with indefinite quadratic terms	3
A posteriori error estimations of the Petrov-Galerkin methods for fractional Helmholtz equations	3
Convergence and stability of extended BBVMs for nonlinear delay-differential-algebraic equations with piecewise continuous arguments	3
A coarsening algorithm on adaptive red-green-blue refined meshes	3
Three decoupled, second-order accurate, and energy stable schemes for the conserved Allen–Cahn-type block copolymer (BCP) model	3
On the generalized AOR and CG iteration methods for a class of block two-by-two linear systems	3
A simple extrapolation method for clustered eigenvalues	3
Analytical and numerical solution techniques for a class of time-fractional integro-partial differential equations	3
A complex structure-preserving algorithm for the full rank decomposition of quaternion matrices and its applications	3
Gradient and diagonal Hessian approximations using quadratic interpolation models and aligned regular bases	3
Generating the Laguerre expansion coefficients by solving a one-dimensional transport equation	3
On the backward Euler method for a generalized Ait-Sahalia-type rate model with Poisson jumps	3
Computational and theoretical aspects of Romanovski-Bessel polynomials and their applications in spectral approximations	3
A proximal bundle-based algorithm for nonsmooth constrained multiobjective optimization problems with inexact data	3
Fast and reliable high-accuracy computation of Gauss–Jacobi quadrature	3
Artificial compressibility SAV ensemble algorithms for the incompressible Navier-Stokes equations	3
An infeasible interior-point arc-search algorithm for nonlinear constrained optimization	3
Two-grid finite element method for the dual-permeability-Stokes fluid flow model	3
Global error estimation for explicit second derivative general linear methods	3
Arbitrary high-order linearly implicit energy-preserving algorithms for Hamiltonian PDEs	3
Second derivative backward differentiation formulae for ODEs based on barycentric rational interpolants	3
A truncated Clenshaw-Curtis formula approximates integrals over a semi-infinite interval	3
Deviation maximization for rank-revealing QR factorizations	3
Unconditional optimal error estimates of linearized backward Euler Galerkin FEMs for nonlinear Schrödinger-Helmholtz equations	3
Adjusting the energy of Ball surfaces by modifying unfixed control balls	3
A new step size rule for the superiorization method and its application in computerized tomography	3
A high-order numerical scheme for multidimensional convection-diffusion-reaction equation with time-fractional derivative	3
Numerical computation of the coefficients in exponential fitting	3
Representations of generalized inverses via full-rank QDR decomposition	3
Adaptive total variation and second-order total variation-based model for low-rank tensor completion	3
A novel numerical scheme for time-fractional Black-Scholes PDE governing European options in mathematical finance	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
Analysis of two new parareal algorithms based on the Dirichlet-Neumann/Neumann-Neumann waveform relaxation method for the heat equation	3