Numerical Algorithms

Article	Citations
A hybrid three-term conjugate gradient projection method for constrained nonlinear monotone equations with applications	54
Inertial methods for finding minimum-norm solutions of the split variational inequality problem beyond monotonicity	52
An algorithm for best rational approximation based on barycentric rational interpolation	36
Analysis of fractal dimension of mixed Riemann-Liouville integral	34
α-robust error analysis of a mixed finite element method for a time-fractional biharmonic equation	31
Inertial projection-type methods for solving pseudomonotone variational inequality problems in Hilbert space	26
A new family of hybrid three-term conjugate gradient methods with applications in image restoration	26
Dai–Liao extensions of a descent hybrid nonlinear conjugate gradient method with application in signal processing	23
Fast second-order time two-mesh mixed finite element method for a nonlinear distributed-order sub-diffusion model	23
On a fast deterministic block Kaczmarz method for solving large-scale linear systems	22
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	21
On two-subspace randomized extended Kaczmarz method for solving large linear least-squares problems	20
A modulus-based formulation for the vertical linear complementarity problem	19
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	19
A new self-adaptive algorithm for solving the split common fixed point problem with multiple output sets in Hilbert spaces	18
A space-time finite element method for solving linear Riesz space fractional partial differential equations	18
Finite volume approach for fragmentation equation and its mathematical analysis	17
Step-by-step solving schemes based on scalar auxiliary variable and invariant energy quadratization approaches for gradient flows	17
Temporal second-order difference methods for solving multi-term time fractional mixed diffusion and wave equations	17
Highly efficient schemes for time-fractional Allen-Cahn equation using extended SAV approach	17
Linearly compact scheme for 2D Sobolev equation with Burgers’ type nonlinearity	15
Two second-order and linear numerical schemes for the multi-dimensional nonlinear time-fractional Schrödinger equation	15
$$H^{1}$$-norm error analysis of a robust ADI method on graded mesh for three-dimensional subdiffusion problems	15
Generalized cross validation for ℓp-ℓq minimization	14
Faster randomized block sparse Kaczmarz by averaging	13

A novel high-order numerical scheme and its analysis for the two-dimensional time-fractional reaction-subdiffusion equation	13
A modified inertial three-term conjugate gradient projection method for constrained nonlinear equations with applications in compressed sensing	13
Energy dissipation–preserving time-dependent auxiliary variable method for the phase-field crystal and the Swift–Hohenberg models	13
The studies of the linearly modified energy-preserving finite difference methods applied to solve two-dimensional nonlinear coupled wave equations	12
Bernstein super fractal interpolation function for countable data systems	12
Dimensions of new fractal functions and associated measures	12
Error bounds for septic Hermite interpolation and its implementation to study modified Burgers’ equation	12
A first-order inexact primal-dual algorithm for a class of convex-concave saddle point problems	11
Local and parallel finite element methods based on two-grid discretizations for the nonstationary Navier-Stokes equations	11
Two modified inertial projection algorithms for bilevel pseudomonotone variational inequalities with applications to optimal control problems	11
Global algorithm for a class of multiplicative programs using piecewise linear approximation technique	11
Revisiting subgradient extragradient methods for solving variational inequalities	11
Filtered interpolation for solving Prandtl’s integro-differential equations	11
Supercloseness and postprocessing for linear finite element method on Bakhvalov-type meshes	10
On the convergence of Krylov methods with low-rank truncations	10
Adaptive Euler methods for stochastic systems with non-globally Lipschitz coefficients	10
Dynamics of Newton-like root finding methods	10
A new computational method based on fractional Lagrange functions to solve multi-term fractional differential equations	10
Two-grid finite element methods for nonlinear time-fractional parabolic equations	10
A two-parameter block triangular preconditioner for double saddle point problem arising from liquid crystal directors modeling	10
An upwind DG scheme preserving the maximum principle for the convective Cahn-Hilliard model	9
Newton method for ℓ0-regularized optimization	9
A minimum-time obstacle-avoidance path planning algorithm for unmanned aerial vehicles	9
A Tseng extragradient method for solving variational inequality problems in Banach spaces	9
A priori and a posteriori error analysis for virtual element discretization of elliptic optimal control problem	9
Inertial accelerated primal-dual methods for linear equality constrained convex optimization problems	9
Modulus-based synchronous multisplitting iteration methods for large sparse vertical linear complementarity problems	9
Convergence of the Nelder-Mead method	9
The conservative characteristic difference method and analysis for solving two-sided space-fractional advection-diffusion equations	9
Second-order maximum principle preserving Strang’s splitting schemes for anisotropic fractional Allen-Cahn equations	9
A simple yet efficient two-step fifth-order weighted-Newton method for nonlinear models	9
Convergence analysis of sample average approximation for a class of stochastic nonlinear complementarity problems: from two-stage to multistage	9
A novel numerical scheme for time-fractional Black-Scholes PDE governing European options in mathematical finance	8
Centrality measures for node-weighted networks via line graphs and the matrix exponential	8
Fully numerical Laplace transform methods	8
Generalized conformable fractional Newton-type method for solving nonlinear systems	8
Accurate error estimation in CG	8
Crank-Nicolson ADI finite difference/compact difference schemes for the 3D tempered integrodifferential equation associated with Brownian motion	8
New modulus-based matrix splitting methods for implicit complementarity problem	8
The strong convergence and stability of explicit approximations for nonlinear stochastic delay differential equations	8
Analysis of two variants of an inertial projection algorithm for finding the minimum-norm solutions of variational inequality and fixed point problems	8
A solely time-dependent source reconstruction in a multiterm time-fractional order diffusion equation with non-smooth solutions	8
Solving decomposable sparse systems	8
A method of fundamental solutions for heat and wave propagation from lateral Cauchy data	8
Anymatrix: an extensible MATLAB matrix collection	8
Unconditionally optimal H1-error estimate of a fast nonuniform L2-1σ scheme for nonlinear subdiffusion equations	8
Adaptive three-term PRP algorithms without gradient Lipschitz continuity condition for nonconvex functions	8
Arbitrarily high-order energy-conserving methods for Poisson problems	8
Continuation Newton methods with the residual trust-region time-stepping scheme for nonlinear equations	7
Second-order IMEX scheme for a system of partial integro-differential equations from Asian option pricing under regime-switching jump-diffusion models	7

Fast Toeplitz eigenvalue computations, joining interpolation-extrapolation matrix-less algorithms and simple-loop theory	7
A class of new Magnus-type methods for semi-linear non-commutative Itô stochastic differential equations	7
Completely discrete schemes for 2D Sobolev equations with Burgers’ type nonlinearity	7
Balanced-norm error estimate of the local discontinuous Galerkin method on layer-adapted meshes for reaction-diffusion problems	7
On the best achievable quality of limit points of augmented Lagrangian schemes	7
Superconvergence analysis of BDF-Galerkin FEM for nonlinear Schrödinger equation	7
Finite element method for singularly perturbed problems with two parameters on a Bakhvalov-type mesh in 2D	7
A subgradient proximal method for solving a class of monotone multivalued variational inequality problems	7
Global error estimation for explicit general linear methods	7
A new proximal-like algorithm for solving split variational inclusion problems	7
Improved splitting preconditioner for double saddle point problems arising from liquid crystal director modeling	7
An efficient algorithm for solving piecewise-smooth dynamical systems	7
Accurate and stable numerical method based on the Floater-Hormann interpolation for stochastic Itô-Volterra integral equations	7
A new optimal root-finding iterative algorithm: local and semilocal analysis with polynomiography	7
Mathematical programs with vanishing constraints involving strongly invex functions	7
A second-order finite difference scheme for the multi-dimensional nonlinear time-fractional Schrödinger equation	7
Sharp error estimate of a Grünwald–Letnikov scheme for reaction-subdiffusion equations	7
Total positivity and accurate computations with Gram matrices of Bernstein bases	6
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	6
Finite difference formulas in the complex plane	6
Accelerated dynamical approaches for finding the unique positive solution of $\mathcal {K}\mathcal {S}$-tensor equations	6
Substructured two-grid and multi-grid domain decomposition methods	6
A complex structure-preserving algorithm for the full rank decomposition of quaternion matrices and its applications	6
Perturbation analysis and condition numbers of mixed least squares-scaled total least squares problem	6
Fitted schemes for Caputo-Hadamard fractional differential equations	6
A numerical method based on Legendre wavelet and quasilinearization technique for fractional Lane-Emden type equations	6
A dynamic distributed conjugate gradient method for variational inequality problem over the common fixed-point constraints	6
Galerkin finite element method for nonlinear fractional differential equations	6
A proximal bundle-based algorithm for nonsmooth constrained multiobjective optimization problems with inexact data	6
BEM-Fading regularization algorithm for Cauchy problems in 2D anisotropic heat conduction	6
A note on memory-less SR1 and memory-less BFGS methods for large-scale unconstrained optimization	6
An efficient Gauss–Newton algorithm for solving regularized total least squares problems	6
A new multi-step method for solving nonlinear systems with high efficiency indices	6
A Hessenberg-type algorithm for computing PageRank Problems	6
A fast second-order predictor-corrector method for a nonlinear time-fractional Benjamin-Bona-Mahony-Burgers equation	6
Numerical approximations to a singularly perturbed convection-diffusion problem with a discontinuous initial condition	6
Weak convergence of Euler scheme for SDEs with low regular drift	6
A high-order numerical scheme for multidimensional convection-diffusion-reaction equation with time-fractional derivative	6
Two-step modulus-based matrix splitting iteration methods for retinex problem	6
Enhanced moving least squares method for solving the stochastic fractional Volterra integro-differential equations of Hammerstein type	6
A fast time two-mesh finite volume element algorithm for the nonlinear time-fractional coupled diffusion model	6
Perron communicability and sensitivity of multilayer networks	6
Efficient difference method for time-space fractional diffusion equation with Robin fractional derivative boundary condition	6
Projected explicit and implicit Taylor series methods for DAEs	6
The joint bidiagonalization process with partial reorthogonalization	6
A primal-dual splitting algorithm for composite monotone inclusions with minimal lifting	5
Analytical and numerical solution techniques for a class of time-fractional integro-partial differential equations	5
A uniformly accurate exponential wave integrator Fourier pseudo-spectral method with structure-preservation for long-time dynamics of the Dirac equation with small potentials	5
A numerical study on the N-periodic wave solutions of two coupled bilinear equations	5
A τ-preconditioner for a non-symmetric linear system arising from multi-dimensional Riemann-Liouville fractional diffusion equation	5
All-at-once method for variable-order time fractional diffusion equations	5
Modified third and fifth order WENO schemes for inviscid compressible flows	5
Numerical study on Moore-Penrose inverse of tensors via Einstein product	5
An adaptive mesh refinement method for indirectly solving optimal control problems	5
Regularized minimal-norm solution of an overdetermined system of first kind integral equations	5
Local and parallel stabilized finite element methods based on two-grid discretizations for the Stokes equations	5
Deviation maximization for rank-revealing QR factorizations	5
Systematic implementation of higher order Whitney forms in methods based on discrete exterior calculus	5
Local and parallel partition of unity scheme for the mixed Navier-Stokes-Darcy problem	5
Relationship between time-instant number and precision of ZeaD formulas with proofs	5
Highly scalable hybrid domain decomposition method for the solution of huge scalar variational inequalities	5
A mixed virtual element method for the time-fractional fourth-order subdiffusion equation	5
Computing Gaussian quadrature rules with high relative accuracy	5
Derivative-free superiorization: principle and algorithm	5
Novel projection methods for solving variational inequality problems and applications	5
Fractional-order Chelyshkov wavelet method for solving variable-order fractional differential equations and an application in variable-order fractional relaxation system	5
A note on stability and fractal dimension of bivariate α-fractal functions	5
Shift-splitting fixed point iteration method for solving generalized absolute value equations	5
The global convergence of the BFGS method with a modified WWP line search for nonconvex functions	5
Tensor theta norms and low rank recovery	5
Fast and accurate solvers for weakly singular integral equations	5
Numerical algorithms for inverse Sturm-Liouville problems	5
Extrapolated sequential constraint method for variational inequality over the intersection of fixed-point sets	5
Modified three-term derivative-free projection method for solving nonlinear monotone equations with application	5
A robust numerical algorithm on harmonic mesh for parabolic singularly perturbed convection-diffusion problems with time delay	5
RBF–DQ algorithms for elliptic problems in axisymmetric domains	5
Mittag–Leffler stability of numerical solutions to time fractional ODEs	5
A preconditioned general modulus-based matrix splitting iteration method for solving horizontal linear complementarity problems	4
Randomized block Krylov subspace algorithms for low-rank quaternion matrix approximations	4
Two-grid finite element method for the dual-permeability-Stokes fluid flow model	4

Integrability and geometry of the Wynn recurrence	4
An hp-version fractional collocation method for Volterra integro-differential equations with weakly singular kernels	4
A new branch-and-cut algorithm for non-convex quadratic programming via alternative direction method and semidefinite relaxation	4
A second-order finite difference scheme for nonlinear tempered fractional integrodifferential equations in three dimensions	4
On condition numbers of the total least squares problem with linear equality constraint	4
Wavelet regularization strategy for the fractional inverse diffusion problem	4
A posteriori error estimation for quasilinear singularly perturbed problems with integral boundary condition	4
Numerical solution to a nonlinear McKendrick-Von Foerster equation with diffusion	4
Third-order accurate, large time-stepping and maximum-principle-preserving schemes for the Allen-Cahn equation	4
On the generalized AOR and CG iteration methods for a class of block two-by-two linear systems	4
Globally convergent diagonal Polak–Ribière–Polyak like algorithm for nonlinear equations	4
Gradient and diagonal Hessian approximations using quadratic interpolation models and aligned regular bases	4
Computational and theoretical aspects of Romanovski-Bessel polynomials and their applications in spectral approximations	4
Error estimates of finite difference methods for the Dirac equation in the massless and nonrelativistic regime	4
Improved Gegenbauer spectral tau algorithms for distributed-order time-fractional telegraph models in multi-dimensions	4
Up to eighth-order maximum-principle-preserving methods for the Allen–Cahn equation	4
Stability analysis of the method of fundamental solutions with smooth closed pseudo-boundaries for Laplace’s equation: better pseudo-boundaries	4
Drift-implicit Euler scheme for sandwiched processes driven by Hölder noises	4
A superconvergent ultra-weak local discontinuous Galerkin method for nonlinear fourth-order boundary-value problems	4
An algebraically stabilized method for convection–diffusion–reaction problems with optimal experimental convergence rates on general meshes	4
Finding global minima with an inflection point-based filled function algorithm	4
Efficient parameter-robust numerical methods for singularly perturbed semilinear parabolic PDEs of convection-diffusion type	4
High order multiquadric trigonometric quasi-interpolation method for solving time-dependent partial differential equations	4
Virtual element method for nonlinear Sobolev equation on polygonal meshes	4
A highly efficient and accurate new SAV approach for the modified phase field crystal model	4
Off-diagonal symmetric nonnegative matrix factorization	4
Relaxed Tseng splitting method with double inertial steps for solving monotone inclusions and fixed point problems	4
A generalized cyclic iterative method for solving variational inequalities over the solution set of a split common fixed point problem	4
Implicit algorithms for eigenvector nonlinearities	4
A numerical method for the approximation of stable and unstable manifolds of microscopic simulators	4
Comment on: “A derivative-free iterative method for nonlinear monotone equations with convex constraints”	4
A hybrid inertial and contraction proximal point algorithm for monotone variational inclusions	4
On the L$$^{\infty }$$ convergence of a novel fourth-order compact and conservative difference scheme for the generalized Rosenau-KdV-RLW equation	4
A matrix splitting preconditioning method for solving the discretized tempered fractional diffusion equations	4
Lattice Boltzmann Method Analysis Tool (LBMAT)	4
Interpolation of sparse high-dimensional data	4
A variant of PMHSS iteration method for a class of complex symmetric indefinite linear systems	4
Inverse central ordering for the Newton interpolation formula	4
A second-order decoupled algorithm with different subdomain time steps for the non-stationary Stokes/Darcy model	4
A null-space approach for large-scale symmetric saddle point systems with a small and non zero (2, 2) block	4
A novel method to approximate fractional differential equations based on the theory of functional connections	4
Optimal convergence of three iterative methods based on nonconforming finite element discretization for 2D/3D MHD equations	4
Discrete comparison principle of a finite difference method for the multi-term time fractional diffusion equation	4
A simple extrapolation method for clustered eigenvalues	4
Fully decoupled, linear, and energy-preserving GSAV difference schemes for the nonlocal coupled sine-Gordon equations in multiple dimensions	4
Parameter estimation for time-fractional Black-Scholes equation with S &P 500 index option	4
A sample efficient sparse FFT for arbitrary frequency candidate sets in high dimensions	4
A numerical implementation for the high-order 2D virtual element method in MATLAB	4
A high-order adaptive numerical algorithm for fractional diffusion wave equation on non-uniform meshes	4
Dual descent regularization algorithms in variable exponent Lebesgue spaces for imaging	4
A class of blending functions with $C^{\infty }$ smoothness	4
(Spectral) Chebyshev collocation methods for solving differential equations	4
A second-order dynamical system for equilibrium problems	4
Enabling four-dimensional conformal hybrid meshing with cubic pyramids	3
The generalized quadrature method for a class of highly oscillatory Volterra integral equations	3
Global error estimation for explicit second derivative general linear methods	3
Analysis of Schwarz waveform relaxation for the coupled Ekman boundary layer problem with continuously variable coefficients	3
A unified approach to Krylov subspace methods for solving linear systems	3
Uniform stability for a spatially discrete, subdiffusive Fokker–Planck equation	3
Strong convergence of Bregman projection method for solving variational inequality problems in reflexive Banach spaces	3
A highly efficient class of optimal fourth-order methods for solving nonlinear systems	3
Two-dimensional Laplace transform inversion using bivariate homogeneous two-point Padé approximants	3
A strong sequential optimality condition for cardinality-constrained optimization problems	3
Two-grid method for compressible miscible displacement problem by mixed finite element methods and expanded mixed finite element method of characteristics	3
Relaxed fixed point iterations for matrix equations arising in Markov chain modeling	3
Efficient quadrature rules for the singularly oscillatory Bessel transforms and their error analysis	3
Oscillation-preserving Legendre-Galerkin methods for second kind integral equations with highly oscillatory kernels	3
Convergence of modulus-based matrix splitting iteration method for a class of nonlinear complementarity problems	3
A low-rank solution method for Riccati equations with indefinite quadratic terms	3
Higher-order recurrence relations, Sobolev-type inner products and matrix factorizations	3
On the viscosity approximation type iterative method and its non-linear behaviour in the generation of Mandelbrot and Julia sets	3
Adjusting the energy of Ball surfaces by modifying unfixed control balls	3
A μ-mode BLAS approach for multidimensional tensor-structured problems	3
Direct serendipity and mixed finite elements on convex polygons	3
Conformable vector Traub’s method for solving nonlinear systems	3
An EMC-HDG scheme for the convection-diffusion equation with random diffusivity	3
Superconvergence results for non-linear Hammerstein integral equations on unbounded domain	3
Strong convergence and extinction of positivity preserving explicit scheme for the stochastic SIS epidemic model	3
Optimal error estimate of the penalty method for the 2D/3D time-dependent MHD equations	3
Operator-splitting local discontinuous Galerkin method for multi-dimensional linear convection-diffusion equations	3
A posteriori error estimations of the Petrov-Galerkin methods for fractional Helmholtz equations	3
On an integrated Krylov-ADI solver for large-scale Lyapunov equations	3
An infeasible interior-point arc-search algorithm for nonlinear constrained optimization	3
Uniform convergence of optimal order for a finite element method on a Bakhvalov-type mesh for a singularly perturbed convection-diffusion equation with parabolic layers	3
Arbitrary high-order linearly implicit energy-preserving algorithms for Hamiltonian PDEs	3
A class of new three-term descent conjugate gradient algorithms for large-scale unconstrained optimization and applications to image restoration problems	3
Towards a reliable implementation of least-squares collocation for higher index differential-algebraic equations—Part 1: basics and ansatz function choices	3
Two new self-adaptive algorithms for solving the split feasibility problem in Hilbert space	3
Three decoupled, second-order accurate, and energy stable schemes for the conserved Allen–Cahn-type block copolymer (BCP) model	3
Randomized Kaczmarz method with adaptive stepsizes for inconsistent linear systems	3
On the rational approximation of Markov functions, with applications to the computation of Markov functions of Toeplitz matrices	3
Using a library of chemical reactions to fit systems of ordinary differential equations to agent-based models: a machine learning approach	3
Artificial compressibility SAV ensemble algorithms for the incompressible Navier-Stokes equations	3
Energy-preserving Du Fort-Frankel difference schemes for solving sine-Gordon equation and coupled sine-Gordon equations	3
A new linearized maximum principle preserving and energy stability scheme for the space fractional Allen-Cahn equation	3