Numerical Algorithms

Article	Citations
Uniformly accurate nested Picard iterative integrators for the Klein-Gordon-Schrödinger equation in the nonrelativistic regime	37
Fast solution method and simulation for the 2D time-space fractional Black-Scholes equation governing European two-asset option pricing	37
Correction to: Fitted schemes for Caputo-Hadamard fractional differential equations	36
The linear barycentric rational backward differentiation formulae for stiff ODEs on nonuniform grids	33
New modulus-based matrix splitting methods for implicit complementarity problem	29
Convergence, weak w2 stability, and data dependence results for the F iterative scheme in hyperbolic spaces	27
Positive quadrature formulas on an arc of the unit circle	23
The application of Goeken–Johnson’s Runge–Kutta methods in unconstrained convex optimization	22
ENO-based high-order data-bounded and constrained positivity-preserving interpolation	22
Two novel numerical methods for gradient flows: generalizations of the Invariant Energy Quadratization method	18
The backward rounding error analysis of the quaternion Givens QR decomposition	18
TRIPs-Py: Techniques for regularization of inverse problems in python	17
Modified globally convergent Polak-Ribière-Polyak conjugate gradient methods with self-correcting property for large-scale unconstrained optimization	17
A unified convergence analysis of the derivative-free projection-based method for constrained nonlinear monotone equations	16
Optimal polynomial approximation to rational matrix functions using the Arnoldi algorithm	16
A multipoint flux mixed finite element method with mass-conservative characteristic finite element method for incompressible miscible displacement problem	16
Numerical analysis of a linearly backward Euler method with truncated Wiener process for a stochastic SIS model	16
A two-parameter block triangular preconditioner for double saddle point problem arising from liquid crystal directors modeling	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	15
Modulus-based synchronous multisplitting iteration methods for large sparse vertical linear complementarity problems	15
Several accelerated subspace minimization conjugate gradient methods based on regularization model and convergence rate analysis for nonconvex problems	15
Balanced-norm error estimate of the local discontinuous Galerkin method on layer-adapted meshes for reaction-diffusion problems	15
On the maximal order of convergence of Green’s function method for solving two-point boundary value problems with deviating argument	14
Orthogonal polynomials relative to weight functions of Prudnikov type	14
A spatial branch and bound algorithm for solving the sum of linear ratios optimization problem	13

Interlacing and bounds of zeros of quasi-orthogonal little q-Jacobi polynomials	13
Extrapolation quadrature from equispaced samples of functions with jumps	13
On a class of infinite M-matrices with an extended quasi-Toeplitz structure	13
A modulus-based cascadic multigrid method for elliptic variational inequality problems	13
Modulus-based block triangular splitting iteration method for solving the generalized absolute value equations	13
A simple yet efficient two-step fifth-order weighted-Newton method for nonlinear models	13
Weak convergence of Euler scheme for SDEs with low regular drift	13
Orthogonal Cauchy-like matrices	13
A novel banded preconditioner for coupled tempered fractional diffusion equation generated from the regime-switching CGMY model	12
Solving non-differentiable Hammerstein integral equations via first-order divided differences	12
A mixed precision LOBPCG algorithm	12
High accuracy two-level compact implicit method in exponential form for 2D fourth order quasi-linear parabolic equations	12
Multivariate polynomial interpolation based on Radon projections	12
Numerical solution to the exterior Bernoulli problem using the Dirichlet-Robin energy gap cost functional approach in two and three dimensions	12
Correction to: Alternatives to the EM algorithm for ML estimation of location, scatter matrix, and degree of freedom of the Student t distribution	12
Banded preconditioning with shift compensation for solving discrete Riesz space-fractional diffusion equations	11
High modes smoothing of time schemes for nonlinear parabolic PDEs	11
Maximal residual coordinate descent method with k-means clustering for solving large linear least-squares problems	11
Improvements to steepest descent method for multi-objective optimization	11
A class of new three-term descent conjugate gradient algorithms for large-scale unconstrained optimization and applications to image restoration problems	10
Randomized flexible GMRES with deflated restarting	10
Incomplete double-cone factorizations of centrosymmetric matrices arising in spectral methods	10
On the accurate computation of the Newton form of the Lagrange interpolant	10
Shift-splitting fixed point iteration method for solving generalized absolute value equations	10
Comments on “Fractal functions associated with Reich contractions: an approximation of chaotic attractors”	10
Logarithmic function minimization to compressed sensing with application to magnetic resonance imaging	10
Decompose-then-optimize: a new approach to design domain decomposition methods for optimal control problems	10
Szegő quadrature formulas associated with the weight function $$1+\cos (m\theta )$$ with application to the approximation of certain Christoffel transformations on the interval	10
Fourier transforms of orthogonal polynomials on the cone	10
Vem++, a C++ library to handle and play with the virtual element method	10
Preconditioned inexact fixed point iteration method for solving tensor absolute value equation	10
Total positivity and accurate computations with Gram matrices of Bernstein bases	10
Proximal variable smoothing method for three-composite nonconvex nonsmooth minimization with a linear operator	9
Solving semi-discrete optimal transport problems: star shapedeness and Newton’s method	9
A family of gradient methods using Householder transformation with application to hypergraph partitioning	9
Linear and nonlinear substructured Restricted Additive Schwarz iterations and preconditioning	9
Adaptive cross approximation for Tikhonov regularization in general form	9
Applications of quasideterminants to non-commutative multistep $$\varepsilon $$-algorithm	9
A fast second-order predictor-corrector method for a nonlinear time-fractional Benjamin-Bona-Mahony-Burgers equation	9
Complex moment-based methods for differential eigenvalue problems	9
Global convergence of a spectral conjugate gradient method for unconstrained optimization	9
Polynomial estimates for the method of cyclic projections in Hilbert spaces	9
Averaged cubature schemes on the real positive semiaxis	9
Analysis of the basins of attraction generated by a pseudo Newton-Raphson method iterating over complex order derivatives	9
A multidimensional Hermite-Gauss sampling formula for analytic functions of several variables	9
A numerical method based on Legendre wavelet and quasilinearization technique for fractional Lane-Emden type equations	9
Communication in multiplex transportation networks	9
Higher-order recurrence relations, Sobolev-type inner products and matrix factorizations	9
Maximum bound principle for matrix-valued Allen-Cahn equation and integrating factor Runge-Kutta method	9
Optimal error estimate of the penalty method for the 2D/3D time-dependent MHD equations	8

Correction to: High-order linearly implicit exponential integrators conserving quadratic invariants with application to scalar auxiliary variable approach	8
Exact subdomain and embedded interface polynomial integration in finite elements with planar cuts	8
Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the third and fourth kinds	8
Optimized Schwarz domain decomposition algorithms for the closest point method on closed manifolds	8
Local and parallel stabilized finite element methods based on two-grid discretizations for the Stokes equations	8
Alternated inertial algorithms for split feasibility problems	8
The truncated Euler-Maruyama method for highly nonlinear stochastic differential equations with multiple time delays	8
Smaller stencil preconditioners for linear systems in RBF-FD discretizations	8
A robust variant of cubic smoothing spline approximation	8
Optimal Control problems of NS-$$\alpha $$ and NS-$$\omega $$ turbulence models: analysis and numerical tests	8
First order strong approximation of Ait–Sahalia-type interest rate model with Poisson jumps	8
Fractional-order Chelyshkov wavelet method for solving variable-order fractional differential equations and an application in variable-order fractional relaxation system	8
A two-grid combined mixed finite element and discontinuous Galerkin method for a compressible miscible displacement problem	8
Hybrid coupling of finite element and boundary element methods using Nitsche’s method and the Calderon projection	8
Integrable semi-discretizations and self-adaptive moving mesh method for a generalized sine-Gordon equation	8
Fitted schemes for Caputo-Hadamard fractional differential equations	8
A new approach of shifted Jacobi spectral Galerkin methods (SJSGM) for weakly singular Fredholm integral equation with non-smooth solution	7
Analysis of a higher-order scheme for multi-term time-fractional integro-partial differential equations with multi-term weakly singular kernels	7
Extended explicit Pseudo two-step Runge-Kutta-Nyström methods for general second-order oscillatory systems	7
A non-linear conjugate gradient in dual space for $$L_p$$-norm regularized non-linear least squares with application in data assimilation	7
The behavior of the Gauss-Radau upper bound of the error norm in CG	7
Sliding modes of high codimension in piecewise-smooth dynamical systems	7
Non-blind constraint image deblurring problem with mean curvature functional	7
A variational regularization method for solving the non-characteristic Cauchy problem in multiple dimensions	7
Non-linear WENO B-spline based approximation method	7
H-representation method for the least squares symmetric solutions of the reduced biquaternion matrix equation and its application in color image restoration	7
Computing Gaussian quadrature rules with high relative accuracy	7
A solely time-dependent source reconstruction in a multiterm time-fractional order diffusion equation with non-smooth solutions	7
Fast superconvergent solvers for weakly singular Hammerstein equations	7
Locally conservative discontinuous bubble scheme for Darcy flow and its application to Hele-Shaw equation based on structured grids	7
A stable second-order difference scheme for the generalized time-fractional non-Fickian delay reaction-diffusion equations	7
Piecewise numerical approach for solving piecewise fractional optimal control and variational problems	7
A fault detection method based on partition of unity and kernel approximation	7
On the randomized Euler schemes for ODEs under inexact information	7
A new family of fourth-order energy-preserving integrators	7
Fractional Legendre wavelet approach resolving multi-scale optimal control problems involving Caputo-Fabrizio derivative	7
Runge–Kutta methods determined from extended phase space methods for Hamiltonian systems	7
Unconditionally energy stable IEQ-FEMs for the Cahn-Hilliard equation and Allen-Cahn equation	7
Stochastic incremental mirror descent algorithms with Nesterov smoothing	7
Generalized discrete Lotka-Volterra equation, orthogonal polynomials and generalized epsilon algorithm	7
Correction to: On the best achievable quality of limit points of augmented Lagrangian schemes	7
A Numerical Approach for the System of Nonlinear Variable-order Fractional Volterra Integral Equations	6
Fading regularization MFS algorithm for the Cauchy problem associated with the two-dimensional Stokes equations	6
An efficient numerical algorithm based on Haar wavelets for multi-dimensional nonlinear elliptic PDEs	6
An MP-DWR method for h-adaptive finite element methods	6
A hybrid gradient method for vector optimization problems	6
Revisiting the (block) Jacobi subspace rotation method for the symmetric eigenvalue problem	6
Second-order IMEX scheme for a system of partial integro-differential equations from Asian option pricing under regime-switching jump-diffusion models	6
Estimating error norms in CG-like algorithms for least-squares and least-norm problems	6
The method of randomized Bregman projections for stochastic feasibility problems	6
Non-negative Einstein tensor factorization for unmixing hyperspectral images	6
An incomplete tridiagonalization-based determinant evaluation for a generalized periodic tridiagonal matrix	6
Fully numerical Laplace transform methods	6
A mixed virtual element method for the time-fractional fourth-order subdiffusion equation	6
Unconditional stability and optimal error estimates of a Crank-Nicolson Legendre-Galerkin method for the two-dimensional second-order wave equation	6
An improved preconditioned inexact Uzawa method for elliptic optimal control problems	6
Fast and accurate solvers for weakly singular integral equations	6
Stieltjes interlacing of zeros of little q-Jacobi and q-Laguerre polynomials from different sequences	6
The generalized modular string averaging procedure and its applications to iterative methods for solving various nonlinear operator theory problems	6
Interpolated Galerkin finite elements on rectangular and cuboid meshes for the Poisson equation	6
Nonmonotone Quasi–Newton-based conjugate gradient methods with application to signal processing	6
Unconditionally positivity-preserving approximations of the Aït-Sahalia type model: Explicit Milstein-type schemes	6
Inexact quasi-Newton methods under a relaxed metric regularity assumption	6
Adaptive time step selection for spectral deferred correction	6
Boundary corrections on multi-dimensional PDEs	6
Optimal size of the block in block GMRES on GPUs: computational model and experiments	6
A weak Galerkin finite element method for singularly perturbed problems with two small parameters on Bakhvalov-type meshes	5
Max-convolution through numerics and tropical geometry	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
On computing the zeros of a class of Sobolev orthogonal polynomials	5
The global convergence of the BFGS method with a modified WWP line search for nonconvex functions	5
A new optimal root-finding iterative algorithm: local and semilocal analysis with polynomiography	5
Limited memory gradient methods for unconstrained optimization	5
Accelerated methods with fastly vanishing subgradients for structured non-smooth minimization	5
Fractal interpolation on the real projective plane	5
Error estimates of finite difference methods for the Dirac equation in the massless and nonrelativistic regime	5
RMPIA: a new algorithm for computing the Lagrange matrix interpolation polynomials	5
A novel numerical scheme for time-fractional Black-Scholes PDE governing European options in mathematical finance	5
A fast stable accurate artificial boundary condition for the linearized Green-Naghdi system	5

A high-order numerical scheme and its analysis for Caputo temporal-fractional Black-Scholes model: European double barrier knock-out option	5
A hybrid-inertial accelerated spectral CG projection method with restart mechanism and its application to compressed sensing	5
Global convergence of a curvilinear search for non-convex optimization	5
Some combined techniques of spectral conjugate gradient methods with applications to robotic and image restoration models	5
A nonsmooth Newton method for solving the generalized complementarity problem	5
A projection algorithm for pseudomonotone vector fields with convex constraints on Hadamard manifolds	5
Hermite interpolation theorems for band-limited functions of the linear canonical transforms with equidistant samples	5
A cubic regularization of Newton’s method with finite difference Hessian approximations	5
Tensor Interpolation	5
Fast and low-memory compressive sensing algorithms for low tucker-rank tensor approximation from streamed measurements	5
Two-level methods for solving higher order finite element discretizations of nonsymmetric and indefinite elliptic problem	5
A closest point method library for PDEs on surfaces with parallel domain decomposition solvers and preconditioners	5
Divergence of the Euler-Maruyama method for neutral stochastic differential equations with unbounded delay and Markovian switching	5
Refined and refined harmonic Jacobi–Davidson methods for computing several GSVD components of a large regular matrix pair	5
New structure-preserving algorithms of Gauss-Seidel and successive over-relaxation iteration methods for quaternion linear systems	5
A two-dimensional randomized extended Gauss-Seidel algorithm for solving least squares problems	5
A note on the Grcar matrix	5
A posteriori error estimates for the time-dependent convection-diffusion-reaction equation coupled with the Darcy system	5
On estimating the separation associated with the periodic continuous Sylvester equation	5
An effective computational approach based on new multi-step collocation method for solving integral-algebraic equations	5
Another Hager-Zhang-type method via singular-value study for constrained monotone equations with application	5
Artificial compressibility SAV ensemble algorithms for the incompressible Navier-Stokes equations	5
Explicit numerical methods for solving singular initial value problems for systems of second-order nonlinear ODEs	5
New proximal bundle algorithm based on the gradient sampling method for nonsmooth nonconvex optimization with exact and inexact information	5
A class of modified accelerated proximal gradient methods for nonsmooth and nonconvex minimization problems	5
On the non-global linear stability and spurious fixed points of MPRK schemes with negative RK parameters	5
Optimality and duality results for fractional programming problems under E-univexity	5
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	5
A fast second-order scheme for nonlinear Riesz space-fractional diffusion equations	5
Fractional centered difference schemes and banded preconditioners for nonlinear Riesz space variable-order fractional diffusion equations	4
Quantifying mixing in arbitrary fluid domains: a Padé approximation approach	4
Numerical solution of the boundary value problems for the biharmonic equations via quasiseparable representations	4
The quaternion relaxed greedy randomized Kaczmarz method with adaptive parameters for solving quaternion matrix equation	4
Smooth connectivity in real algebraic varieties	4
Operator-splitting finite element method for solving the radiative transfer equation	4
Numerical solution of distributed-order fractional Korteweg-de Vries equation via fractional Zigzag rising diagonal functions	4
An efficient fractional step numerical algorithm for time-delayed singularly perturbed 2D convection-diffusion–reaction problem with two small parameters	4
A second-order BDF convex splitting numerical scheme for the Ericksen-Leslie equation	4
Mixed noise removal via generalized gaussian scale mixture modeling and plug-and-play deep prior	4
A posteriori error estimations of the Petrov-Galerkin methods for fractional Helmholtz equations	4
Accelerated iterative algorithms for the Cauchy problem in steady-state anisotropic heat conduction	4
Network analysis with the aid of the path length matrix	4
Lagrange interpolation polynomials for solving nonlinear stochastic integral equations	4
Variable parameter Uzawa method for solving the indefinite least squares problem	4
An inexact proximal majorization-minimization algorithm for remote sensing image stripe noise removal	4
Quantitative analysis of a subgradient-type method for equilibrium problems	4
Cocoercivity, smoothness and bias in variance-reduced stochastic gradient methods	4
On Hölder global optimization method using piecewise affine bounding functions	4
Approximation operators explored through the lens of degenerate hermite polynomials	4
Fractional filter method for recovering the historical distribution for diffusion equations with coupling operator of local and nonlocal type	4
Strong convergence of Bregman projection method for solving variational inequality problems in reflexive Banach spaces	4
The condition number of many tensor decompositions is invariant under Tucker compression	4
A highly efficient class of optimal fourth-order methods for solving nonlinear systems	4
Computing eigenvalues of semi-infinite quasi-Toeplitz matrices	4
Modified projection method and strong convergence theorem for solving variational inequality problems with non-Lipschitz operators	4
Correction to: fast and accurate numerical algorithm for solving stochastic itô-volterra integral equations	4
Novel numerical methods based on graded, adaptive and uniform meshes for a time-fractional advection-diffusion equation subjected to weakly singular solution	4
The semi-implicit DLN algorithm for the Navier-Stokes equations	4
Inertial accelerated primal-dual methods for linear equality constrained convex optimization problems	4
Another HSS iteration method	4
Existence results and numerical method for solving a fourth-order nonlinear integro-differential equation	4
Approximation by polynomials in Sobolev spaces associated with classical moment functionals	4
Reducing the truncation error in Taylor model multiplication	4
An adaptive mesh refinement method for indirectly solving optimal control problems	4
Finite element approximation of optimal control problem with integral fractional Laplacian and state constraint	4
A third-order iterative algorithm for inversion of cumulative central beta distribution	4
A novel high-order numerical scheme and its analysis for the two-dimensional time-fractional reaction-subdiffusion equation	4
A μ-mode BLAS approach for multidimensional tensor-structured problems	4
Fast Euler–Maruyama method for weakly singular stochastic Volterra integral equations with variable exponent	4
Fast and stable rational approximation of generalized hypergeometric functions	4
On multivariate orthogonal polynomials and elementary symmetric functions	4
Equivalence and convergence analysis of fixed point iterative schemes using higher order averaged mappings	4
A Riemannian inexact Newton dogleg method for constructing a symmetric nonnegative matrix with prescribed spectrum	4
C-FISTA type projection algorithm for quasi-variational inequalities	4
HODLR3D: hierarchical matrices for N-body problems in three dimensions	4
Two new self-adaptive algorithms for solving the split feasibility problem in Hilbert space	4
Inertial self-adaptive algorithms for solving non-smooth convex optimization problems	4
A free parameter dependent family of polynomial wavelets on a compact interval	4
Inertial-type incremental constraint projection method for solving variational inequalities without Lipschitz continuity	4
Edge importance in complex networks	4
Relaxed Tseng splitting method with double inertial steps for solving monotone inclusions and fixed point problems	4
Cut-edge centralities in an undirected graph	4
The explicit form of the vector $$\varepsilon $$-algorithm’s kernel : a conjecture and its solution in $$\mathbb {R}^4 $$	4
$$O(1/k^2)$$ convergence rates of (dual-primal) balanced augmented Lagrangian methods for linearly constrained convex programming	4
Quantile-based random sparse Kaczmarz for corrupted and noisy linear systems	4
Numerical analysis of penalty–based ensemble methods	4
Deviation maximization for rank-revealing QR factorizations	4
On the convergence of Galerkin methods for auto-convolution Volterra integro-differential equations	4
Acceleration of sequences with transformations involving hypergeometric functions	4
Recovering a space-dependent source term for distributed order time-space fractional diffusion equation	3
The strong convergence and stability of explicit approximations for nonlinear stochastic delay differential equations	3
A priori and a posteriori error analysis for virtual element discretization of elliptic optimal control problem	3
An efficient class of Traub-Steffensen-type optimal order multiple root solvers	3
Quasi-Newton interior point method for solving nonlinear system of equations with box constraints	3
An algorithm for approximating implicit functions by polynomials without using higher order differentiability information	3