Numerical Algorithms

Papers
(The median citation count of Numerical Algorithms is 1. The table below lists those papers that are above that threshold based on CrossRef citation counts [max. 250 papers]. The publications cover those that have been published in the past four years, i.e., from 2021-08-01 to 2025-08-01.)
ArticleCitations
Fast solution method and simulation for the 2D time-space fractional Black-Scholes equation governing European two-asset option pricing43
Uniformly accurate nested Picard iterative integrators for the Klein-Gordon-Schrödinger equation in the nonrelativistic regime41
Correction to: Fitted schemes for Caputo-Hadamard fractional differential equations38
The linear barycentric rational backward differentiation formulae for stiff ODEs on nonuniform grids31
A unified convergence analysis of the derivative-free projection-based method for constrained nonlinear monotone equations28
Positive quadrature formulas on an arc of the unit circle27
ENO-based high-order data-bounded and constrained positivity-preserving interpolation23
The backward rounding error analysis of the quaternion Givens QR decomposition20
The application of Goeken–Johnson’s Runge–Kutta methods in unconstrained convex optimization20
Two novel numerical methods for gradient flows: generalizations of the Invariant Energy Quadratization method19
Convergence, weak w2 stability, and data dependence results for the F iterative scheme in hyperbolic spaces18
Numerical analysis of a linearly backward Euler method with truncated Wiener process for a stochastic SIS model17
Reducing swamp behavior for the canonical polyadic decomposition problem by rank-1 freezing17
Modified globally convergent Polak-Ribière-Polyak conjugate gradient methods with self-correcting property for large-scale unconstrained optimization17
Several accelerated subspace minimization conjugate gradient methods based on regularization model and convergence rate analysis for nonconvex problems16
A multipoint flux mixed finite element method with mass-conservative characteristic finite element method for incompressible miscible displacement problem16
Implementation of divided differences to shape preservation16
Modulus-based synchronous multisplitting iteration methods for large sparse vertical linear complementarity problems16
On the dynamics of Steffensen’s family of root-finding methods for entire function16
Local and parallel finite element methods based on two-grid discretizations for the unsteady mixed Stokes-Darcy model with the Beavers-Joseph interface condition16
TRIPs-Py: Techniques for regularization of inverse problems in python15
New modulus-based matrix splitting methods for implicit complementarity problem15
Optimal polynomial approximation to rational matrix functions using the Arnoldi algorithm15
On the maximal order of convergence of Green’s function method for solving two-point boundary value problems with deviating argument14
On a class of infinite M-matrices with an extended quasi-Toeplitz structure14
Interlacing and bounds of zeros of quasi-orthogonal little q-Jacobi polynomials14
Regularized Barzilai-Borwein Method14
Balanced-norm error estimate of the local discontinuous Galerkin method on layer-adapted meshes for reaction-diffusion problems14
A spatial branch and bound algorithm for solving the sum of linear ratios optimization problem14
Weak convergence of Euler scheme for SDEs with low regular drift14
Extrapolation quadrature from equispaced samples of functions with jumps13
High accuracy two-level compact implicit method in exponential form for 2D fourth order quasi-linear parabolic equations13
Fourier transforms of orthogonal polynomials on the cone13
A novel banded preconditioner for coupled tempered fractional diffusion equation generated from the regime-switching CGMY model13
Solving non-differentiable Hammerstein integral equations via first-order divided differences12
Maximal residual coordinate descent method with k-means clustering for solving large linear least-squares problems12
Modulus-based block triangular splitting iteration method for solving the generalized absolute value equations12
Decompose-then-optimize: a new approach to design domain decomposition methods for optimal control problems12
High modes smoothing of time schemes for nonlinear parabolic PDEs12
Banded preconditioning with shift compensation for solving discrete Riesz space-fractional diffusion equations12
Total positivity and accurate computations with Gram matrices of Bernstein bases12
Improvements to steepest descent method for multi-objective optimization12
Orthogonal polynomials relative to weight functions of Prudnikov type12
On the accurate computation of the Newton form of the Lagrange interpolant12
Correction to: “Patch area and uniform sampling on the surface of any ellipsoid”11
Numerical solution to the exterior Bernoulli problem using the Dirichlet-Robin energy gap cost functional approach in two and three dimensions11
A simple yet efficient two-step fifth-order weighted-Newton method for nonlinear models11
Randomized flexible GMRES with deflated restarting11
Shift-splitting fixed point iteration method for solving generalized absolute value equations11
Multivariate polynomial interpolation based on Radon projections11
A class of new three-term descent conjugate gradient algorithms for large-scale unconstrained optimization and applications to image restoration problems11
Szegő quadrature formulas associated with the weight function $$1+\cos (m\theta )$$ with application to the approximation of certain Christoffel transformations on the interval11
Logarithmic function minimization to compressed sensing with application to magnetic resonance imaging10
Orthogonal Cauchy-like matrices10
Local and parallel stabilized finite element methods based on two-grid discretizations for the Stokes equations10
Vem++, a C++ library to handle and play with the virtual element method10
Incomplete double-cone factorizations of centrosymmetric matrices arising in spectral methods10
Proximal variable smoothing method for three-composite nonconvex nonsmooth minimization with a linear operator10
A modulus-based cascadic multigrid method for elliptic variational inequality problems10
A mixed precision LOBPCG algorithm10
Complex moment-based methods for differential eigenvalue problems9
A fast second-order predictor-corrector method for a nonlinear time-fractional Benjamin-Bona-Mahony-Burgers equation9
Communication in multiplex transportation networks9
Adaptive cross approximation for Tikhonov regularization in general form9
Optimal Control problems of NS-$$\alpha $$ and NS-$$\omega $$ turbulence models: analysis and numerical tests9
Linear and nonlinear substructured Restricted Additive Schwarz iterations and preconditioning9
A family of gradient methods using Householder transformation with application to hypergraph partitioning9
Analysis of the basins of attraction generated by a pseudo Newton-Raphson method iterating over complex order derivatives9
Applications of quasideterminants to non-commutative multistep $$\varepsilon $$-algorithm9
Averaged cubature schemes on the real positive semiaxis9
Fractional-order Chelyshkov wavelet method for solving variable-order fractional differential equations and an application in variable-order fractional relaxation system9
Optimal error estimate of the penalty method for the 2D/3D time-dependent MHD equations9
A multidimensional Hermite-Gauss sampling formula for analytic functions of several variables9
Global convergence of a spectral conjugate gradient method for unconstrained optimization9
Polynomial estimates for the method of cyclic projections in Hilbert spaces9
Optimized Schwarz domain decomposition algorithms for the closest point method on closed manifolds9
Higher-order recurrence relations, Sobolev-type inner products and matrix factorizations9
Preconditioned inexact fixed point iteration method for solving tensor absolute value equation8
Greedy adaptive local recovery of functions in Sobolev spaces8
Exact subdomain and embedded interface polynomial integration in finite elements with planar cuts8
Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the third and fourth kinds8
Comments on “Fractal functions associated with Reich contractions: an approximation of chaotic attractors”8
First order strong approximation of Ait–Sahalia-type interest rate model with Poisson jumps8
Correction to: High-order linearly implicit exponential integrators conserving quadratic invariants with application to scalar auxiliary variable approach8
Smaller stencil preconditioners for linear systems in RBF-FD discretizations8
A robust variant of cubic smoothing spline approximation8
Maximum bound principle for matrix-valued Allen-Cahn equation and integrating factor Runge-Kutta method8
Integrable semi-discretizations and self-adaptive moving mesh method for a generalized sine-Gordon equation8
Fitted schemes for Caputo-Hadamard fractional differential equations8
A two-grid combined mixed finite element and discontinuous Galerkin method for a compressible miscible displacement problem8
Hybrid coupling of finite element and boundary element methods using Nitsche’s method and the Calderon projection8
A numerical method based on Legendre wavelet and quasilinearization technique for fractional Lane-Emden type equations8
Solving semi-discrete optimal transport problems: star shapedeness and Newton’s method8
Accurate inverses and determinants of doubly strictly diagonally dominant Z-matrices7
Fractional Legendre wavelet approach resolving multi-scale optimal control problems involving Caputo-Fabrizio derivative7
Constructing Sobolev orthonormal rational functions via an updating procedure7
A solely time-dependent source reconstruction in a multiterm time-fractional order diffusion equation with non-smooth solutions7
Inertial Bregman proximal gradient under partial smoothness7
Interpolation preservation of AMF-W methods for linear diffusion problems7
Generalized discrete Lotka-Volterra equation, orthogonal polynomials and generalized epsilon algorithm7
A stable second-order difference scheme for the generalized time-fractional non-Fickian delay reaction-diffusion equations7
Fast superconvergent solvers for weakly singular Hammerstein equations7
A variational regularization method for solving the non-characteristic Cauchy problem in multiple dimensions7
Alternated inertial algorithms for split feasibility problems7
Analysis of a higher-order scheme for multi-term time-fractional integro-partial differential equations with multi-term weakly singular kernels7
Comprehensive deep contrastive manifold regularized non-negative matrix factorization for multi-view clustering7
Non-linear WENO B-spline based approximation method7
Legendre polynomial based approximation of the Hessian for quasi-Newton optimization7
On the randomized Euler schemes for ODEs under inexact information7
Stochastic incremental mirror descent algorithms with Nesterov smoothing7
A fault detection method based on partition of unity and kernel approximation7
The behavior of the Gauss-Radau upper bound of the error norm in CG7
Runge–Kutta methods determined from extended phase space methods for Hamiltonian systems7
The truncated Euler-Maruyama method for highly nonlinear stochastic differential equations with multiple time delays7
A new approach of shifted Jacobi spectral Galerkin methods (SJSGM) for weakly singular Fredholm integral equation with non-smooth solution7
A new modified Mann-type method for solving the monotone inclusion problem and the fixed point problem in reflexive Banach spaces7
Extended explicit Pseudo two-step Runge-Kutta-Nyström methods for general second-order oscillatory systems7
Computing Gaussian quadrature rules with high relative accuracy7
A new family of fourth-order energy-preserving integrators7
Sliding modes of high codimension in piecewise-smooth dynamical systems7
A mixed virtual element method for the time-fractional fourth-order subdiffusion equation7
Locally conservative discontinuous bubble scheme for Darcy flow and its application to Hele-Shaw equation based on structured grids7
H-representation method for the least squares symmetric solutions of the reduced biquaternion matrix equation and its application in color image restoration7
A non-linear conjugate gradient in dual space for $$L_p$$-norm regularized non-linear least squares with application in data assimilation7
Correction to: On the best achievable quality of limit points of augmented Lagrangian schemes6
An incomplete tridiagonalization-based determinant evaluation for a generalized periodic tridiagonal matrix6
Unconditionally positivity-preserving approximations of the Aït-Sahalia type model: Explicit Milstein-type schemes6
Fully numerical Laplace transform methods6
Non-negative Einstein tensor factorization for unmixing hyperspectral images6
An improved preconditioned inexact Uzawa method for elliptic optimal control problems6
Optimal polynomial smoothers for parallel AMG6
Fading regularization MFS algorithm for the Cauchy problem associated with the two-dimensional Stokes equations6
Nonmonotone Quasi–Newton-based conjugate gradient methods with application to signal processing6
Piecewise numerical approach for solving piecewise fractional optimal control and variational problems6
Non-blind constraint image deblurring problem with mean curvature functional6
An efficient numerical algorithm based on Haar wavelets for multi-dimensional nonlinear elliptic PDEs6
Interpolated Galerkin finite elements on rectangular and cuboid meshes for the Poisson equation6
Revisiting the (block) Jacobi subspace rotation method for the symmetric eigenvalue problem6
Adaptive time step selection for spectral deferred correction6
Unconditional stability and optimal error estimates of a Crank-Nicolson Legendre-Galerkin method for the two-dimensional second-order wave equation6
Stochastic parareal algorithm for stochastic differential equations6
An MP-DWR method for h-adaptive finite element methods6
A robust Legendre collocation scheme and convergence analysis for Lane-Emden multi-pantograph delay differential equations arising in stellar physics including Chandrasekhar’s white dwarf problem6
Unconditionally energy stable IEQ-FEMs for the Cahn-Hilliard equation and Allen-Cahn equation6
A hybrid gradient method for vector optimization problems6
New proximal bundle algorithm based on the gradient sampling method for nonsmooth nonconvex optimization with exact and inexact information6
Stieltjes interlacing of zeros of little q-Jacobi and q-Laguerre polynomials from different sequences6
Inexact quasi-Newton methods under a relaxed metric regularity assumption6
On computing the zeros of a class of Sobolev orthogonal polynomials5
New structure-preserving algorithms of Gauss-Seidel and successive over-relaxation iteration methods for quaternion linear systems5
Explicit numerical methods for solving singular initial value problems for systems of second-order nonlinear ODEs5
An effective computational approach based on new multi-step collocation method for solving integral-algebraic equations5
Limited memory gradient methods for unconstrained optimization5
Optimal size of the block in block GMRES on GPUs: computational model and experiments5
A class of modified accelerated proximal gradient methods for nonsmooth and nonconvex minimization problems5
A fast second-order scheme for nonlinear Riesz space-fractional diffusion equations5
A new optimal root-finding iterative algorithm: local and semilocal analysis with polynomiography5
Two-level methods for solving higher order finite element discretizations of nonsymmetric and indefinite elliptic problem5
Artificial compressibility SAV ensemble algorithms for the incompressible Navier-Stokes equations5
Some combined techniques of spectral conjugate gradient methods with applications to robotic and image restoration models5
Fractal interpolation on the real projective plane5
A conformable fractional iterative fixed-point method for solving one-dimensional nonlinear equations5
A two-dimensional randomized extended Gauss-Seidel algorithm for solving least squares problems5
Refined and refined harmonic Jacobi–Davidson methods for computing several GSVD components of a large regular matrix pair5
Fast and low-memory compressive sensing algorithms for low tucker-rank tensor approximation from streamed measurements5
On the non-global linear stability and spurious fixed points of MPRK schemes with negative RK parameters5
A nonsmooth Newton method for solving the generalized complementarity problem5
A weak Galerkin finite element method for singularly perturbed problems with two small parameters on Bakhvalov-type meshes5
Tensor Interpolation5
A high-order numerical scheme and its analysis for Caputo temporal-fractional Black-Scholes model: European double barrier knock-out option5
Accelerated methods with fastly vanishing subgradients for structured non-smooth minimization5
Fast and accurate solvers for weakly singular integral equations5
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 applications5
The generalized modular string averaging procedure and its applications to iterative methods for solving various nonlinear operator theory problems5
A fast algorithm for time-fractional diffusion equation with space-time-dependent variable order5
Global convergence of a curvilinear search for non-convex optimization5
A note on the Grcar matrix5
Another Hager-Zhang-type method via singular-value study for constrained monotone equations with application5
A hybrid-inertial accelerated spectral CG projection method with restart mechanism and its application to compressed sensing5
The method of randomized Bregman projections for stochastic feasibility problems5
A projection algorithm for pseudomonotone vector fields with convex constraints on Hadamard manifolds5
A cubic regularization of Newton’s method with finite difference Hessian approximations5
The global convergence of the BFGS method with a modified WWP line search for nonconvex functions5
Max-convolution through numerics and tropical geometry5
On estimating the separation associated with the periodic continuous Sylvester equation5
Strong convergence and extinction of positivity preserving explicit scheme for the stochastic SIS epidemic model5
A fourth-order collocation scheme for generalized Black-Scholes model in financial decision-making5
A novel numerical scheme for time-fractional Black-Scholes PDE governing European options in mathematical finance5
Boundary corrections on multi-dimensional PDEs5
On the convergence of two-step modified Newton method for nonsymmetric algebraic Riccati equations from transport theory5
Estimating error norms in CG-like algorithms for least-squares and least-norm problems5
Hermite interpolation theorems for band-limited functions of the linear canonical transforms with equidistant samples5
A Numerical Approach for the System of Nonlinear Variable-order Fractional Volterra Integral Equations5
Divergence of the Euler-Maruyama method for neutral stochastic differential equations with unbounded delay and Markovian switching5
An efficient fractional step numerical algorithm for time-delayed singularly perturbed 2D convection-diffusion–reaction problem with two small parameters4
On the convergence of Galerkin methods for auto-convolution Volterra integro-differential equations4
Lagrange interpolation polynomials for solving nonlinear stochastic integral equations4
Variable parameter Uzawa method for solving the indefinite least squares problem4
Cut-edge centralities in an undirected graph4
A novel high-order numerical scheme and its analysis for the two-dimensional time-fractional reaction-subdiffusion equation4
Finite element approximation of optimal control problem with integral fractional Laplacian and state constraint4
Quantile-based random sparse Kaczmarz for corrupted and noisy linear systems4
A μ-mode BLAS approach for multidimensional tensor-structured problems4
An adaptive mesh refinement method for indirectly solving optimal control problems4
Quantifying mixing in arbitrary fluid domains: a Padé approximation approach4
A third-order iterative algorithm for inversion of cumulative central beta distribution4
The quaternion relaxed greedy randomized Kaczmarz method with adaptive parameters for solving quaternion matrix equation4
Another HSS iteration method4
A Riemannian inexact Newton dogleg method for constructing a symmetric nonnegative matrix with prescribed spectrum4
Analytical and numerical studies of the modified Kawahara equation with dual-power law nonlinearities4
A highly efficient class of optimal fourth-order methods for solving nonlinear systems4
Numerical solution of the boundary value problems for the biharmonic equations via quasiseparable representations4
Two new self-adaptive algorithms for solving the split feasibility problem in Hilbert space4
Inertial-type incremental constraint projection method for solving variational inequalities without Lipschitz continuity4
$$O(1/k^2)$$ convergence rates of (dual-primal) balanced augmented Lagrangian methods for linearly constrained convex programming4
Fractional centered difference schemes and banded preconditioners for nonlinear Riesz space variable-order fractional diffusion equations4
Equivalence and convergence analysis of fixed point iterative schemes using higher order averaged mappings4
Smooth connectivity in real algebraic varieties4
Reducing the truncation error in Taylor model multiplication4
The condition number of many tensor decompositions is invariant under Tucker compression4
A fast stable accurate artificial boundary condition for the linearized Green-Naghdi system4
Quantitative analysis of a subgradient-type method for equilibrium problems4
Acceleration of sequences with transformations involving hypergeometric functions4
Nitsche’s method under a semi-regular mesh condition4
Deviation maximization for rank-revealing QR factorizations4
Approximation operators explored through the lens of degenerate hermite polynomials4
Optimality and duality results for fractional programming problems under E-univexity4
Existence results and numerical method for solving a fourth-order nonlinear integro-differential equation4
HODLR3D: hierarchical matrices for N-body problems in three dimensions4
Novel numerical methods based on graded, adaptive and uniform meshes for a time-fractional advection-diffusion equation subjected to weakly singular solution4
Inertial self-adaptive algorithms for solving non-smooth convex optimization problems4
Modified projection method and strong convergence theorem for solving variational inequality problems with non-Lipschitz operators4
Network analysis with the aid of the path length matrix4
Operator-splitting finite element method for solving the radiative transfer equation4
Relaxed Tseng splitting method with double inertial steps for solving monotone inclusions and fixed point problems4
Strong convergence of Bregman projection method for solving variational inequality problems in reflexive Banach spaces4
On multivariate orthogonal polynomials and elementary symmetric functions4
An inexact proximal majorization-minimization algorithm for remote sensing image stripe noise removal4
Cocoercivity, smoothness and bias in variance-reduced stochastic gradient methods4
On Hölder global optimization method using piecewise affine bounding functions4
Numerical analysis of penalty–based ensemble methods4
Fast and stable rational approximation of generalized hypergeometric functions4
The explicit form of the vector $$\varepsilon $$-algorithm’s kernel : a conjecture and its solution in $$\mathbb {R}^4 $$4
A closest point method library for PDEs on surfaces with parallel domain decomposition solvers and preconditioners4
Fast Euler–Maruyama method for weakly singular stochastic Volterra integral equations with variable exponent4
A second-order BDF convex splitting numerical scheme for the Ericksen-Leslie equation4
Optimal error estimate of fully discrete HDG-IEQ scheme for the general type Cahn-Hilliard equation4
Correction to: fast and accurate numerical algorithm for solving stochastic itô-volterra integral equations4
Role extraction by matrix equations and generalized random walks4
The semi-implicit DLN algorithm for the Navier-Stokes equations4
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