Numerical Algorithms

Article	Citations
A real unconstrained equivalent problem of the quaternion equality constrained weighted least squares problem	36
Solving third-order tensor linear complementarity problems via modulus-based methods and applications	31
A second order non-uniform IMEX-Alikhanov-FEM for time-fractional PDEs and PIDEs with time-dependent coefficients	31
A two-parameter block triangular preconditioner for double saddle point problem arising from liquid crystal directors modeling	30
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	29
A posteriori error estimates for the time-dependent convection-diffusion-reaction equation coupled with the Darcy system	28
An edgewise iterative scheme for the discontinuous Galerkin method with Lagrange multiplier for Poisson’s equation	27
A feasible proximal bundle algorithm with convexification for nonsmooth, nonconvex semi-infinite programming	24
A modified generalized version of projected reflected gradient method in Hilbert spaces	22
A bidiagonalization-based numerical algorithm for computing the inverses of (p,q)-tridiagonal matrices	22
Finding global minima with an inflection point-based filled function algorithm	20
A novel numerical scheme for time-fractional Black-Scholes PDE governing European options in mathematical finance	20
Efficient second-order, linear, decoupled and unconditionally energy stable schemes of the Cahn-Hilliard-Darcy equations for the Hele-Shaw flow	18
Stability improvements for fast matrix multiplication	16
Fast solution method and simulation for the 2D time-space fractional Black-Scholes equation governing European two-asset option pricing	16
On estimating the separation associated with the periodic continuous Sylvester equation	16
A fast and high-order IMEX method for non-linear time-space-fractional reaction-diffusion equations	16
A multipoint flux mixed finite element method with mass-conservative characteristic finite element method for incompressible miscible displacement problem	15
Oscillation-preserving Legendre-Galerkin methods for second kind integral equations with highly oscillatory kernels	15
Local and parallel finite element methods based on two-grid discretizations for the unsteady mixed Stokes-Darcy model with the Beavers-Joseph interface condition	14
Fractional Tikhonov regularization and error estimation in inverse source problems for Biharmonic equations: a priori and a posteriori analysis under deterministic and random perturbations	14
A Modified Iteration Method for an Inverse Problem of Diffusion Equation with Laplace and Riesz-Feller Space Fractional Operators	14
A novel meshless approach based on new fractional spaces for solving nonlinear Riesz space distributed order reaction-diffusion equations with non-smooth solutions and stability analysis	13
Local and parallel partition of unity scheme for the mixed Navier-Stokes-Darcy problem	13
Some combined techniques of spectral conjugate gradient methods with applications to robotic and image restoration models	13

Refined and refined harmonic Jacobi–Davidson methods for computing several GSVD components of a large regular matrix pair	13
Convergence of the Nelder-Mead method	13
Unconditionally convergent and superconvergent finite element method for nonlinear time-fractional parabolic equations with distributed delay	13
Operational Jacobi Galerkin method for a class of cordial Volterra integral equations	13
Preconditioned golden ratio primal-dual algorithm with linesearch	12
Solution of the Cauchy problem for the Brinkman equations using an alternating method of fundamental solutions	12
The linear barycentric rational backward differentiation formulae for stiff ODEs on nonuniform grids	12
The backward rounding error analysis of the quaternion Givens QR decomposition	11
A sign-based linear method for horizontal linear complementarity problems	11
Spectral characterizations and integer powers of tridiagonal 2-Toeplitz matrices	11
A rotated shift-splitting method for complex symmetric linear systems	11
A priori and a posteriori error estimation for singularly perturbed delay integro-differential equations	11
Two-grid finite element method for the dual-permeability-Stokes fluid flow model	11
Variable stepsize general linear methods for ODEs	11
Fixed-time TGNN model with the nonlinear activation function for online solution of Sylvester tensor equation	11
A fast second-order absorbing boundary condition for the linearized Benjamin-Bona-Mahony equation	10
An Uzawa-DOS method for solving saddle-point problems	10
Convergence analysis of the augmented Lagrangian method for $$\ell _{p}$$-norm cone optimization problems with $$p \ge 2$$	10
A note on the Grcar matrix	10
Delay-dependent stability of a class of Runge-Kutta methods for neutral differential equations	10
Two-level methods for solving higher order finite element discretizations of nonsymmetric and indefinite elliptic problem	10
On the rational approximation of Markov functions, with applications to the computation of Markov functions of Toeplitz matrices	10
The application of Goeken–Johnson’s Runge–Kutta methods in unconstrained convex optimization	10
Convergence analysis of Picard–SP iteration process for generalized $$\alpha $$–nonexpansive mappings	10
A strong sequential optimality condition for cardinality-constrained optimization problems	10
The global convergence of the BFGS method with a modified WWP line search for nonconvex functions	10
Two novel numerical methods for gradient flows: generalizations of the Invariant Energy Quadratization method	10
A novel higher-order efficient computational method for pricing European and Asian options	9
Anderson accelerating the preconditioned modulus approach for linear complementarity problems on second-order cones	9
Artificial compressibility SAV ensemble algorithms for the incompressible Navier-Stokes equations	9
A uniformly accurate exponential wave integrator Fourier pseudo-spectral method with structure-preservation for long-time dynamics of the Dirac equation with small potentials	9
An inertial spectral conjugate gradient projection method for constrained nonlinear pseudo-monotone equations	9
Uniformly accurate nested Picard iterative integrators for the Klein-Gordon-Schrödinger equation in the nonrelativistic regime	9
Balanced-norm error estimate of the local discontinuous Galerkin method on layer-adapted meshes for reaction-diffusion problems	9
Parallel strategies for Direct Multisearch	9
Max-convolution through numerics and tropical geometry	9
On the non-global linear stability and spurious fixed points of MPRK schemes with negative RK parameters	9
Computation of incomplete beta function ratios $$I_{x}(a,b)$$ with Deuflhard’s algorithm	9
A minimum-time obstacle-avoidance path planning algorithm for unmanned aerial vehicles	9
The generalized quadrature method for a class of highly oscillatory Volterra integral equations	9
An hp-version fractional collocation method for Volterra integro-differential equations with weakly singular kernels	9
Positive quadrature formulas on an arc of the unit circle	9
A matrix splitting preconditioning method for solving the discretized tempered fractional diffusion equations	9
A new proximal-like algorithm for solving split variational inclusion problems	8
Uncoupling evolutionary groundwater-surface water flows: stabilized mixed methods in both porous media and fluid regions	8
Automatic approximation using asymptotically optimal adaptive interpolation	8
Crank-Nicolson ADI finite difference/compact difference schemes for the 3D tempered integrodifferential equation associated with Brownian motion	8
Discussions on a macro multi-time scales coupling method: existence and uniqueness of the numerical solution and strict non-negativity of the Schur complement	8
A class of modified accelerated proximal gradient methods for nonsmooth and nonconvex minimization problems	8
A limited-memory BFGS-based differential evolution algorithm for optimal control of nonlinear systems with mixed control variables and probability constraints	8

A fast Fourier-Galerkin method solving boundary integral equations for the Helmholtz equation with exponential convergence	8
Certified Newton schemes for the evaluation of low-genus theta functions	8
Relaxed fixed point iterations for matrix equations arising in Markov chain modeling	8
Simultaneous perturbation stochastic approximation: towards one-measurement per iteration	8
A low-rank solution method for Riccati equations with indefinite quadratic terms	8
New structure-preserving algorithms of Gauss-Seidel and successive over-relaxation iteration methods for quaternion linear systems	8
Convergence analysis of sample average approximation for a class of stochastic nonlinear complementarity problems: from two-stage to multistage	8
A convex splitting method for the time-dependent Ginzburg-Landau equation	8
Hermite interpolation theorems for band-limited functions of the linear canonical transforms with equidistant samples	8
A Tseng extragradient method for solving variational inequality problems in Banach spaces	8
Nitsche’s method for elliptic Dirichlet boundary control problems on curved domains	7
Efficient high-order exponential time differencing methods for nonlinear fractional differential models	7
Continuation Newton methods with deflation techniques for global optimization problems	7
An Edge-based cascadic multigrid method for $$H(\textbf{curl})$$ problems	7
Global convergence of a curvilinear search for non-convex optimization	7
Accelerated methods with fastly vanishing subgradients for structured non-smooth minimization	7
Numerical analysis of a linearly backward Euler method with truncated Wiener process for a stochastic SIS model	7
An adaptively preconditioned multi-step matrix splitting iteration for computing PageRank	7
The error estimations of a two-level linearized compact ADI method for solving the nonlinear coupled wave equations	7
On an integrated Krylov-ADI solver for large-scale Lyapunov equations	7
Detection and correction of silent errors in the conjugate gradient algorithm	7
A proper orthogonal decomposition-compact difference algorithm for plate vibration models	7
Spurious eigenvalue-free algorithms of the method of fundamental solutions for solving the Helmholtz equation in bounded multiply connected domains	7
Bernstein super fractal interpolation function for countable data systems	7
Stability analysis of the method of fundamental solutions with smooth closed pseudo-boundaries for Laplace’s equation: better pseudo-boundaries	7
On zero behavior of higher-order Sobolev-type discrete $$q-$$Hermite I orthogonal polynomials	7
The parameterized accelerated iteration method for solving the matrix equation $$AXB=C$$	7
Interpretation of parareal as a two-level additive Schwarz in time preconditioner and its acceleration with GMRES	7
A null-space approach for large-scale symmetric saddle point systems with a small and non zero (2, 2) block	7
On the robustness of exponential base terms and the Padé denominator in some least squares sense	7
A superconvergent ultra-weak local discontinuous Galerkin method for nonlinear fourth-order boundary-value problems	6
The gamma function via interpolation	6
An Ulm-like algorithm for generalized inverse eigenvalue problems	6
Multigrid methods for time fractional conservation laws	6
Dynamics of Newton-like root finding methods	6
Modulus-based synchronous multisplitting iteration methods for large sparse vertical linear complementarity problems	6
A Chebyshev-Markov-Stieltjes separation type theorem for classical Romberg quadrature	6
Inverse central ordering for the Newton interpolation formula	6
A priori error estimates of a discontinuous Galerkin method for the Navier-Stokes equations	6
Fast algorithms for interpolation and smoothing for a general class of fourth order exponential splines	6
Spatial two-grid compact difference method for nonlinear Volterra integro-differential equation with Abel kernel	6
ENO-based high-order data-bounded and constrained positivity-preserving interpolation	6
RBF-FD based some implicit-explicit methods for pricing option under regime-switching jump-diffusion model with variable coefficients	6
A projection algorithm for pseudomonotone vector fields with convex constraints on Hadamard manifolds	6
Error profile for discontinuous Galerkin time stepping of parabolic PDEs	6
Generalized weak Galerkin finite element method for linear elasticity interface problems	6
Extensions of Clenshaw-Curtis-type rules to integrals over a semi-infinite interval	6
Numerical analysis of incompressible wormhole propagation with mass-preserving characteristic mixed finite element procedure	6
Systematic implementation of higher order Whitney forms in methods based on discrete exterior calculus	6
Sharp error estimate of a Grünwald–Letnikov scheme for reaction-subdiffusion equations	6
An Hermite–Obreshkov method for 2nd-order linear initial-value problems for ODE	6
Tensor randomized extended Kaczmarz methods for large inconsistent tensor linear equations with t-product	6
A recursive algorithm for an efficient and accurate computation of incomplete Bessel functions	6
Discrete generalized-Sylvester matrix equation solved by RNN with a novel direct discretization numerical method	6
A unified convergence analysis of the derivative-free projection-based method for constrained nonlinear monotone equations	6
Improved two-step Newton’s method for computing simple multiple zeros of polynomial systems	6
On the convergence of the numerical blow-up time for a rescaling algorithm	6
Modified globally convergent Polak-Ribière-Polyak conjugate gradient methods with self-correcting property for large-scale unconstrained optimization	6
The detection and correction of silent errors in pipelined Krylov subspace methods	5
A proximal bundle-based algorithm for nonsmooth constrained multiobjective optimization problems with inexact data	5
A family of linearly weighted-$$\theta $$ compact ADI schemes for sine-Gordon equations in high dimensions	5
New modulus-based matrix splitting methods for implicit complementarity problem	5
Strong convergence and extinction of positivity preserving explicit scheme for the stochastic SIS epidemic model	5
A fast algorithm for time-fractional diffusion equation with space-time-dependent variable order	5
Globally linearly convergent nonlinear conjugate gradients without Wolfe line search	5
An explicit subgradient extragradient algorithm with self-adaptive stepsize for pseudomonotone equilibrium problems in Banach spaces	5
On the randomized multiple row-action methods for solving linear least-squares problems	5
An effective computational approach based on new multi-step collocation method for solving integral-algebraic equations	5
A high-order numerical scheme for multidimensional convection-diffusion-reaction equation with time-fractional derivative	5
Adaptive discontinuous Galerkin finite element methods for the Allen-Cahn equation on polygonal meshes	5
A fast second-order scheme for nonlinear Riesz space-fractional diffusion equations	5
A sine transform based preconditioned MINRES method for all-at-once systems from constant and variable-coefficient evolutionary PDEs	5
Operator-splitting local discontinuous Galerkin method for multi-dimensional linear convection-diffusion equations	5
A weak Galerkin finite element method for singularly perturbed problems with two small parameters on Bakhvalov-type meshes	5
Correction to: Fitted schemes for Caputo-Hadamard fractional differential equations	5
Convergence, weak w2 stability, and data dependence results for the F iterative scheme in hyperbolic spaces	5
Inexpensive guaranteed and efficient upper bounds on the algebraic error in finite element discretizations	5
TRIPs-Py: Techniques for regularization of inverse problems in python	5
A high-order numerical scheme and its analysis for Caputo temporal-fractional Black-Scholes model: European double barrier knock-out option	5
Two postprocessing techniques for barycentric rational collocation methods applied to weakly singular VIEs	5

A method of fundamental solutions for heat and wave propagation from lateral Cauchy data	5
On solving 2D weakly singular Volterra integral equations of the second kind	5
Linearly compact scheme for 2D Sobolev equation with Burgers’ type nonlinearity	5
Self-adaptive subgradient extragradient algorithm for solving equilibrium and fixed point problems in hilbert spaces	5
A preconditioned general modulus-based matrix splitting iteration method for solving horizontal linear complementarity problems	5
Multivariate quadrature rules on crosslet sparse grids	5
Several accelerated subspace minimization conjugate gradient methods based on regularization model and convergence rate analysis for nonconvex problems	5
Fractal interpolation on the real projective plane	5
Improved uniform error bounds of Lawson-type exponential integrator method for long-time dynamics of the high-dimensional space fractional sine-Gordon equation	5
Hybrid iterative refined restarted Lanczos bidiagonalization methods	5
Generalizing Frobenius inversion to quaternion matrices	5
Decompose-then-optimize: a new approach to design domain decomposition methods for optimal control problems	4
Arbitrarily high-order energy-conserving methods for Poisson problems	4
ANODE 2023 In honour of John Butcher’s 90th birthday	4
Arithmetical enhancements of the Kogbetliantz method for the SVD of order two	4
N-mode minimal tensor extrapolation methods	4
Stationary iterated weighted Tikhonov regularization method for identifying an unknown source term of time-fractional radial heat equation	4
A modified local and parallel finite element method for the coupled Stokes-Darcy model with the Beavers-Joseph interface condition	4
RMPIA: a new algorithm for computing the Lagrange matrix interpolation polynomials	4
A numerical approach for solving fractional order pantograph mixed Volterra-Fredholm delay-integro-differential equations	4
Jacobi spectral projection methods for Fredholm integral equations of the first kind	4
Operator-splitting finite element method for solving the radiative transfer equation	4
Efficient quaternion CUR method for low-rank approximation to quaternion matrix	4
An inertial Hestenes-Stiefel algorithm for nonsmooth convex optimization and its applications in machine learning	4
A reliable numerical algorithm mixed with hypergeometric function for analyzing fractional variational problems	4
A fast stable accurate artificial boundary condition for the linearized Green-Naghdi system	4
Anti-Gaussian quadrature rules related to orthogonality on the semicircle	4
Cut-edge centralities in an undirected graph	4
Complex structure-preserving method for Schrödinger equations in quaternionic quantum mechanics	4
A multi-physical structure-preserving method and its analysis for the conservative Allen-Cahn equation with nonlocal constraint	4
C-FISTA type projection algorithm for quasi-variational inequalities	4
A dynamic distributed conjugate gradient method for variational inequality problem over the common fixed-point constraints	4
In reference to a self-referential approach towards smooth multivariate approximation	4
Solving non-differentiable Hammerstein integral equations via first-order divided differences	4
A fast construction algorithm for compact singular value decomposition of dual quaternion matrix and its application	4
A high-order adaptive numerical algorithm for fractional diffusion wave equation on non-uniform meshes	4
Comment on: “A derivative-free iterative method for nonlinear monotone equations with convex constraints”	4
Modified projection method and strong convergence theorem for solving variational inequality problems with non-Lipschitz operators	4
Extended homogeneous bivariate orthogonal polynomials: symbolic and numerical Gaussian cubature formula	4
Extrapolation methods for multilinear PageRank	4
On the maximal order of convergence of Green’s function method for solving two-point boundary value problems with deviating argument	4
$$L^2$$ norm convergence of IMEX BDF2 scheme with variable-step for the incompressible Navier-Stokes equations	4
Correction to: Alternatives to the EM algorithm for ML estimation of location, scatter matrix, and degree of freedom of the Student t distribution	4
Strong and linear convergence of projection-type method with an inertial term for finding minimum-norm solutions of pseudomonotone variational inequalities in Hilbert spaces	4
An ensemble scheme for the numerical solution of a random transient heat equation with uncertain inputs	4
Maximal residual coordinate descent method with k-means clustering for solving large linear least-squares problems	4
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	4
A new linearized maximum principle preserving and energy stability scheme for the space fractional Allen-Cahn equation	4
Numerical solution of two-dimensional Hammerstein integral equations via quadratic spline collocation	4
Differential equation software for the computation of error-controlled continuous approximate solutions	4
Inexact asymmetric forward-backward-adjoint splitting algorithms for saddle point problems	4
Accelerated iterative algorithms for the Cauchy problem in steady-state anisotropic heat conduction	4
Error analysis of a high-order fully discrete method for two-dimensional time-fractional convection-diffusion equations exhibiting weak initial singularity	4
Multiscale matrix pencils for separable reconstruction problems	4
Richard Steven Varga, 1928–2022	4
Detecting and approximating decision boundaries in low-dimensional spaces	4
Implicit–explicit two–step peer methods with RK stability for implicit part	4
A mass- and energy-conserved DG method for the Schrödinger-Poisson equation	4
Improvements to steepest descent method for multi-objective optimization	4
Two formulae with nodes related to zeros of Bessel functions for semi-infinite integrals: extending Gauss–Jacobi-type rules	4
Randomized Kaczmarz method with adaptive stepsizes for inconsistent linear systems	4
Revisiting subgradient extragradient methods for solving variational inequalities	4
Interlacing and bounds of zeros of quasi-orthogonal little q-Jacobi polynomials	4
Analytical and numerical solution techniques for a class of time-fractional integro-partial differential equations	4
A spatial branch and bound algorithm for solving the sum of linear ratios optimization problem	4
A second-order finite difference scheme for the multi-dimensional nonlinear time-fractional Schrödinger equation	4
A posteriori error bounds for the block-Lanczos method for matrix function approximation	4
Error estimates of finite difference methods for the Dirac equation in the massless and nonrelativistic regime	3
On semilocal convergence analysis for two-step Newton method under generalized Lipschitz conditions in Banach spaces	3
Generalized second derivative linear multistep methods for ordinary differential equations	3
A closest point method library for PDEs on surfaces with parallel domain decomposition solvers and preconditioners	3
High accuracy two-level compact implicit method in exponential form for 2D fourth order quasi-linear parabolic equations	3
A Lanczos-type procedure for tensors	3
Inertial accelerated primal-dual methods for linear equality constrained convex optimization problems	3
A two-level iterative method with Newton-type linearization for the stationary micropolar fluid equations	3
Modified iterated Crank-Nicolson method with improved accuracy for advection equations	3
A μ-mode BLAS approach for multidimensional tensor-structured problems	3
Computation of polynomial and rational approximations in complex domains by the $$\tau $$-method	3
Iterative methods for solving tensor equations based on exponential acceleration	3
Extrapolation quadrature from equispaced samples of functions with jumps	3
A low-rank update for relaxed Schur complement preconditioners in fluid flow problems	3
A second-order dynamical system for equilibrium problems	3
Computation of the confluent hypergeometric function U(a,b,x) and its derivative for positive arguments	3
Block GPBi-CG method for solving nonsymmetric linear systems with multiple right-hand sides and its convergence analysis	3
Deviation maximization for rank-revealing QR factorizations	3
An efficient numerical method on modified space-time sparse grid for time-fractional diffusion equation with nonsmooth data	3
Upper triangulation-based infinity norm bounds for the inverse of Nekrasov matrices with applications	3
An EMC-HDG scheme for the convection-diffusion equation with random diffusivity	3
Uniform stability for a spatially discrete, subdiffusive Fokker–Planck equation	3
A modulus-based cascadic multigrid method for elliptic variational inequality problems	3
Orthogonal Cauchy-like matrices	3
Novel numerical methods based on graded, adaptive and uniform meshes for a time-fractional advection-diffusion equation subjected to weakly singular solution	3
Completely discrete schemes for 2D Sobolev equations with Burgers’ type nonlinearity	3
Error analysis for the pseudostress formulation of unsteady Stokes problem	3
A primal-dual splitting algorithm for composite monotone inclusions with minimal lifting	3