Numerical Algorithms

Article	Citations
Fast solution method and simulation for the 2D time-space fractional Black-Scholes equation governing European two-asset option pricing	37
Uniformly accurate nested Picard iterative integrators for the Klein-Gordon-Schrödinger equation in the nonrelativistic regime	36
Correction to: Fitted schemes for Caputo-Hadamard fractional differential equations	32
A unified convergence analysis of the derivative-free projection-based method for constrained nonlinear monotone equations	32
The linear barycentric rational backward differentiation formulae for stiff ODEs on nonuniform grids	28
New modulus-based matrix splitting methods for implicit complementarity problem	27
Local and parallel finite element methods based on two-grid discretizations for the unsteady mixed Stokes-Darcy model with the Beavers-Joseph interface condition	26
Convergence, weak w2 stability, and data dependence results for the F iterative scheme in hyperbolic spaces	23
A new proximal-like algorithm for solving split variational inclusion problems	23
Positive quadrature formulas on an arc of the unit circle	22
Several accelerated subspace minimization conjugate gradient methods based on regularization model and convergence rate analysis for nonconvex problems	20
ENO-based high-order data-bounded and constrained positivity-preserving interpolation	18
The application of Goeken–Johnson’s Runge–Kutta methods in unconstrained convex optimization	17
Two novel numerical methods for gradient flows: generalizations of the Invariant Energy Quadratization method	16
The backward rounding error analysis of the quaternion Givens QR decomposition	16
Numerical analysis of a linearly backward Euler method with truncated Wiener process for a stochastic SIS model	16
A multipoint flux mixed finite element method with mass-conservative characteristic finite element method for incompressible miscible displacement problem	15
Modified globally convergent Polak-Ribière-Polyak conjugate gradient methods with self-correcting property for large-scale unconstrained optimization	15
TRIPs-Py: Techniques for regularization of inverse problems in python	15
A two-parameter block triangular preconditioner for double saddle point problem arising from liquid crystal directors modeling	15
Balanced-norm error estimate of the local discontinuous Galerkin method on layer-adapted meshes for reaction-diffusion problems	15
Weak convergence of Euler scheme for SDEs with low regular drift	14
Modulus-based synchronous multisplitting iteration methods for large sparse vertical linear complementarity problems	14
Modulus-based block triangular splitting iteration method for solving the generalized absolute value equations	13
A spatial branch and bound algorithm for solving the sum of linear ratios optimization problem	13

On the maximal order of convergence of Green’s function method for solving two-point boundary value problems with deviating argument	13
A simple yet efficient two-step fifth-order weighted-Newton method for nonlinear models	13
Interlacing and bounds of zeros of quasi-orthogonal little q-Jacobi polynomials	13
Randomized flexible GMRES with deflated restarting	13
On a class of infinite M-matrices with an extended quasi-Toeplitz structure	13
Orthogonal polynomials relative to weight functions of Prudnikov type	13
Extrapolation quadrature from equispaced samples of functions with jumps	12
Numerical solution to the exterior Bernoulli problem using the Dirichlet-Robin energy gap cost functional approach in two and three dimensions	12
Total positivity and accurate computations with Gram matrices of Bernstein bases	12
A modulus-based cascadic multigrid method for elliptic variational inequality problems	12
A mixed precision LOBPCG algorithm	12
Orthogonal Cauchy-like matrices	12
A class of new three-term descent conjugate gradient algorithms for large-scale unconstrained optimization and applications to image restoration problems	12
Multivariate polynomial interpolation based on Radon projections	11
A novel banded preconditioner for coupled tempered fractional diffusion equation generated from the regime-switching CGMY model	11
Correction to: Alternatives to the EM algorithm for ML estimation of location, scatter matrix, and degree of freedom of the Student t distribution	11
On the accurate computation of the Newton form of the Lagrange interpolant	11
Solving non-differentiable Hammerstein integral equations via first-order divided differences	11
High accuracy two-level compact implicit method in exponential form for 2D fourth order quasi-linear parabolic equations	11
Incomplete double-cone factorizations of centrosymmetric matrices arising in spectral methods	10
Improvements to steepest descent method for multi-objective optimization	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
Maximal residual coordinate descent method with k-means clustering for solving large linear least-squares problems	10
Decompose-then-optimize: a new approach to design domain decomposition methods for optimal control problems	10
Vem++, a C++ library to handle and play with the virtual element method	10
High modes smoothing of time schemes for nonlinear parabolic PDEs	10
Banded preconditioning with shift compensation for solving discrete Riesz space-fractional diffusion equations	10
Preconditioned inexact fixed point iteration method for solving tensor absolute value equation	10
A numerical method based on Legendre wavelet and quasilinearization technique for fractional Lane-Emden type equations	9
Local and parallel stabilized finite element methods based on two-grid discretizations for the Stokes equations	9
A multidimensional Hermite-Gauss sampling formula for analytic functions of several variables	9
Solving semi-discrete optimal transport problems: star shapedeness and Newton’s method	9
Applications of quasideterminants to non-commutative multistep $$\varepsilon $$-algorithm	9
First order strong approximation of Ait–Sahalia-type interest rate model with Poisson jumps	9
Optimal error estimate of the penalty method for the 2D/3D time-dependent MHD equations	9
Complex moment-based methods for differential eigenvalue problems	9
Proximal variable smoothing method for three-composite nonconvex nonsmooth minimization with a linear operator	9
Global convergence of a spectral conjugate gradient method for unconstrained optimization	9
Linear and nonlinear substructured Restricted Additive Schwarz iterations and preconditioning	9
Analysis of the basins of attraction generated by a pseudo Newton-Raphson method iterating over complex order derivatives	9
A fast second-order predictor-corrector method for a nonlinear time-fractional Benjamin-Bona-Mahony-Burgers equation	9
Logarithmic function minimization to compressed sensing with application to magnetic resonance imaging	9
Fitted schemes for Caputo-Hadamard fractional differential equations	9
A family of gradient methods using Householder transformation with application to hypergraph partitioning	9
Communication in multiplex transportation networks	9
Polynomial estimates for the method of cyclic projections in Hilbert spaces	9
A robust variant of cubic smoothing spline approximation	8
The truncated Euler-Maruyama method for highly nonlinear stochastic differential equations with multiple time delays	8
Adaptive cross approximation for Tikhonov regularization in general form	8

Maximum bound principle for matrix-valued Allen-Cahn equation and integrating factor Runge-Kutta method	8
Integrable semi-discretizations and self-adaptive moving mesh method for a generalized sine-Gordon equation	8
A non-linear conjugate gradient in dual space for $$L_p$$-norm regularized non-linear least squares with application in data assimilation	8
Extended explicit Pseudo two-step Runge-Kutta-Nyström methods for general second-order oscillatory systems	8
Averaged cubature schemes on the real positive semiaxis	8
Optimized Schwarz domain decomposition algorithms for the closest point method on closed manifolds	8
Alternated inertial algorithms for split feasibility problems	8
Correction to: High-order linearly implicit exponential integrators conserving quadratic invariants with application to scalar auxiliary variable approach	8
Higher-order recurrence relations, Sobolev-type inner products and matrix factorizations	8
Fractional-order Chelyshkov wavelet method for solving variable-order fractional differential equations and an application in variable-order fractional relaxation system	8
Optimal Control problems of NS-$$\alpha $$ and NS-$$\omega $$ turbulence models: analysis and numerical tests	8
On the randomized Euler schemes for ODEs under inexact information	7
H-representation method for the least squares symmetric solutions of the reduced biquaternion matrix equation and its application in color image restoration	7
A variational regularization method for solving the non-characteristic Cauchy problem in multiple dimensions	7
A solely time-dependent source reconstruction in a multiterm time-fractional order diffusion equation with non-smooth solutions	7
Nonmonotone Quasi–Newton-based conjugate gradient methods with application to signal processing	7
A two-grid combined mixed finite element and discontinuous Galerkin method for a compressible miscible displacement problem	7
Exact subdomain and embedded interface polynomial integration in finite elements with planar cuts	7
A new family of fourth-order energy-preserving integrators	7
Piecewise numerical approach for solving piecewise fractional optimal control and variational problems	7
Unconditionally energy stable IEQ-FEMs for the Cahn-Hilliard equation and Allen-Cahn equation	7
Fast superconvergent solvers for weakly singular Hammerstein equations	7
Fractional Legendre wavelet approach resolving multi-scale optimal control problems involving Caputo-Fabrizio derivative	7
Non-linear WENO B-spline based approximation method	7
Locally conservative discontinuous bubble scheme for Darcy flow and its application to Hele-Shaw equation based on structured grids	7
Hybrid coupling of finite element and boundary element methods using Nitsche’s method and the Calderon projection	7
Computing Gaussian quadrature rules with high relative accuracy	7
Analysis of a higher-order scheme for multi-term time-fractional integro-partial differential equations with multi-term weakly singular kernels	7
Correction to: On the best achievable quality of limit points of augmented Lagrangian schemes	7
The behavior of the Gauss-Radau upper bound of the error norm in CG	7
Runge–Kutta methods determined from extended phase space methods for Hamiltonian systems	7
A new approach of shifted Jacobi spectral Galerkin methods (SJSGM) for weakly singular Fredholm integral equation with non-smooth solution	7
Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the third and fourth kinds	7
Smaller stencil preconditioners for linear systems in RBF-FD discretizations	7
Generating the Laguerre expansion coefficients by solving a one-dimensional transport equation	7
A fault detection method based on partition of unity and kernel approximation	6
Generalized discrete Lotka-Volterra equation, orthogonal polynomials and generalized epsilon algorithm	6
A new branch-and-cut algorithm for non-convex quadratic programming via alternative direction method and semidefinite relaxation	6
Fading regularization MFS algorithm for the Cauchy problem associated with the two-dimensional Stokes equations	6
Inexact quasi-Newton methods under a relaxed metric regularity assumption	6
Relationship between time-instant number and precision of ZeaD formulas with proofs	6
Interpolated Galerkin finite elements on rectangular and cuboid meshes for the Poisson equation	6
A mixed virtual element method for the time-fractional fourth-order subdiffusion equation	6
Non-blind constraint image deblurring problem with mean curvature functional	6
Sliding modes of high codimension in piecewise-smooth dynamical systems	6
An efficient numerical algorithm based on Haar wavelets for multi-dimensional nonlinear elliptic PDEs	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
Limited memory gradient methods for unconstrained optimization	6
Unconditional stability and optimal error estimates of a Crank-Nicolson Legendre-Galerkin method for the two-dimensional second-order wave equation	6
Fully numerical Laplace transform methods	6
Stochastic incremental mirror descent algorithms with Nesterov smoothing	6
A stable second-order difference scheme for the generalized time-fractional non-Fickian delay reaction-diffusion equations	6
An MP-DWR method for h-adaptive finite element methods	6
Non-negative Einstein tensor factorization for unmixing hyperspectral images	6
A hybrid gradient method for vector optimization problems	6
Adaptive time step selection for spectral deferred correction	6
Revisiting the (block) Jacobi subspace rotation method for the symmetric eigenvalue problem	6
An incomplete tridiagonalization-based determinant evaluation for a generalized periodic tridiagonal matrix	6
Unconditionally positivity-preserving approximations of the Aït-Sahalia type model: Explicit Milstein-type schemes	6
Optimal size of the block in block GMRES on GPUs: computational model and experiments	5
A cubic regularization of Newton’s method with finite difference Hessian approximations	5
Global convergence of a curvilinear search for non-convex optimization	5
A posteriori error estimates for the time-dependent convection-diffusion-reaction equation coupled with the Darcy system	5
Artificial compressibility SAV ensemble algorithms for the incompressible Navier-Stokes equations	5
Refined and refined harmonic Jacobi–Davidson methods for computing several GSVD components of a large regular matrix pair	5
Some combined techniques of spectral conjugate gradient methods with applications to robotic and image restoration models	5
A projection algorithm for pseudomonotone vector fields with convex constraints on Hadamard manifolds	5
Two-level methods for solving higher order finite element discretizations of nonsymmetric and indefinite elliptic problem	5
Tensor Interpolation	5
Accelerated methods with fastly vanishing subgradients for structured non-smooth minimization	5
A nonsmooth Newton method for solving the generalized complementarity problem	5
Fractal interpolation on the real projective plane	5
New proximal bundle algorithm based on the gradient sampling method for nonsmooth nonconvex optimization with exact and inexact information	5
Estimating error norms in CG-like algorithms for least-squares and least-norm problems	5
Hermite interpolation theorems for band-limited functions of the linear canonical transforms with equidistant samples	5
A fast algorithm for time-fractional diffusion equation with space-time-dependent variable order	5
A hybrid-inertial accelerated spectral CG projection method with restart mechanism and its application to compressed sensing	5
A note on the Grcar matrix	5
A weak Galerkin finite element method for singularly perturbed problems with two small parameters on Bakhvalov-type meshes	5

A fast second-order scheme for nonlinear Riesz space-fractional diffusion equations	5
On estimating the separation associated with the periodic continuous Sylvester equation	5
On the non-global linear stability and spurious fixed points of MPRK schemes with negative RK parameters	5
A new optimal root-finding iterative algorithm: local and semilocal analysis with polynomiography	5
A high-order numerical scheme and its analysis for Caputo temporal-fractional Black-Scholes model: European double barrier knock-out option	5
An improved preconditioned inexact Uzawa method for elliptic optimal control problems	5
An effective computational approach based on new multi-step collocation method for solving integral-algebraic equations	5
Fast and accurate solvers for weakly singular integral equations	5
A Numerical Approach for the System of Nonlinear Variable-order Fractional Volterra Integral Equations	5
The method of randomized Bregman projections for stochastic feasibility problems	5
A class of modified accelerated proximal gradient methods for nonsmooth and nonconvex minimization problems	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
New structure-preserving algorithms of Gauss-Seidel and successive over-relaxation iteration methods for quaternion linear systems	5
Strong convergence and extinction of positivity preserving explicit scheme for the stochastic SIS epidemic model	5
Explicit numerical methods for solving singular initial value problems for systems of second-order nonlinear ODEs	5
The global convergence of the BFGS method with a modified WWP line search for nonconvex functions	5
Another Hager-Zhang-type method via singular-value study for constrained monotone equations with application	5
An explicit subgradient extragradient algorithm with self-adaptive stepsize for pseudomonotone equilibrium problems in Banach spaces	5
A two-dimensional randomized extended Gauss-Seidel algorithm for solving least squares problems	5
Max-convolution through numerics and tropical geometry	5
Second-order IMEX scheme for a system of partial integro-differential equations from Asian option pricing under regime-switching jump-diffusion models	5
Boundary corrections on multi-dimensional PDEs	5
Cut-edge centralities in an undirected graph	4
Quantile-based random sparse Kaczmarz for corrupted and noisy linear systems	4
Acceleration of sequences with transformations involving hypergeometric functions	4
Variable parameter Uzawa method for solving the indefinite least squares problem	4
Quantifying mixing in arbitrary fluid domains: a Padé approximation approach	4
On multivariate orthogonal polynomials and elementary symmetric functions	4
Optimality and duality results for fractional programming problems under E-univexity	4
An adaptive mesh refinement method for indirectly solving optimal control problems	4
A novel numerical scheme for time-fractional Black-Scholes PDE governing European options in mathematical finance	4
Modified projection method and strong convergence theorem for solving variational inequality problems with non-Lipschitz operators	4
Two new self-adaptive algorithms for solving the split feasibility problem in Hilbert space	4
The explicit form of the vector $$\varepsilon $$-algorithm’s kernel : a conjecture and its solution in $$\mathbb {R}^4 $$	4
An inexact proximal majorization-minimization algorithm for remote sensing image stripe noise removal	4
Fast Euler–Maruyama method for weakly singular stochastic Volterra integral equations with variable exponent	4
Reducing the truncation error in Taylor model multiplication	4
Strong convergence of Bregman projection method for solving variational inequality problems in reflexive Banach spaces	4
On the convergence of Galerkin methods for auto-convolution Volterra integro-differential equations	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
On Hölder global optimization method using piecewise affine bounding functions	4
Quantitative analysis of a subgradient-type method for equilibrium problems	4
Fractional filter method for recovering the historical distribution for diffusion equations with coupling operator of local and nonlocal type	4
Existence results and numerical method for solving a fourth-order nonlinear integro-differential equation	4
Deviation maximization for rank-revealing QR factorizations	4
Another HSS iteration method	4
RMPIA: a new algorithm for computing the Lagrange matrix interpolation polynomials	4
Cocoercivity, smoothness and bias in variance-reduced stochastic gradient methods	4
Operator-splitting finite element method for solving the radiative transfer equation	4
Accelerated iterative algorithms for the Cauchy problem in steady-state anisotropic heat conduction	4
Correction to: fast and accurate numerical algorithm for solving stochastic itô-volterra integral equations	4
A posteriori error estimations of the Petrov-Galerkin methods for fractional Helmholtz equations	4
$$O(1/k^2)$$ convergence rates of (dual-primal) balanced augmented Lagrangian methods for linearly constrained convex programming	4
A novel high-order numerical scheme and its analysis for the two-dimensional time-fractional reaction-subdiffusion equation	4
Lagrange interpolation polynomials for solving nonlinear stochastic integral equations	4
The quaternion relaxed greedy randomized Kaczmarz method with adaptive parameters for solving quaternion matrix equation	4
Approximation operators explored through the lens of degenerate hermite polynomials	4
C-FISTA type projection algorithm for quasi-variational inequalities	4
Network analysis with the aid of the path length matrix	4
Error estimates of finite difference methods for the Dirac equation in the massless and nonrelativistic regime	4
An efficient fractional step numerical algorithm for time-delayed singularly perturbed 2D convection-diffusion–reaction problem with two small parameters	4
Fast and stable rational approximation of generalized hypergeometric functions	4
A subgradient proximal method for solving a class of monotone multivalued variational inequality problems	4
A closest point method library for PDEs on surfaces with parallel domain decomposition solvers and preconditioners	4
The condition number of many tensor decompositions is invariant under Tucker compression	4
A fast stable accurate artificial boundary condition for the linearized Green-Naghdi system	4
A Riemannian inexact Newton dogleg method for constructing a symmetric nonnegative matrix with prescribed spectrum	4
A μ-mode BLAS approach for multidimensional tensor-structured problems	4
Edge importance in complex networks	4
Inertial-type incremental constraint projection method for solving variational inequalities without Lipschitz continuity	4
Fractional centered difference schemes and banded preconditioners for nonlinear Riesz space variable-order fractional diffusion 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
Inertial accelerated primal-dual methods for linear equality constrained convex optimization problems	4
Relaxed Tseng splitting method with double inertial steps for solving monotone inclusions and fixed point problems	4
A highly efficient class of optimal fourth-order methods for solving nonlinear systems	4
Numerical analysis of penalty–based ensemble methods	4
A priori and a posteriori error analysis for virtual element discretization of elliptic optimal control problem	3
A matrix-less method to approximate the spectrum and the spectral function of Toeplitz matrices with real eigenvalues	3
Unconditionally optimal H1-error estimate of a fast nonuniform L2-1σ scheme for nonlinear subdiffusion equations	3
Generation of orthogonal rational functions by procedures for structured matrices	3
Correction to: Generalizing Frobenius inversion to quaternion matrices	3
A note on memory-less SR1 and memory-less BFGS methods for large-scale unconstrained optimization	3
A new linearized maximum principle preserving and energy stability scheme for the space fractional Allen-Cahn equation	3
Estimate of transition kernel for Euler-Maruyama scheme for SDEs driven by $$\alpha $$-stable noise and applications	3
Perron communicability and sensitivity of multilayer networks	3
An easy-to-implement recursive fractional spectral-Galerkin method for multi-term weakly singular Volterra integral equations with non-smooth solutions	3
A novel method to approximate fractional differential equations based on the theory of functional connections	3
Enhanced moving least squares method for solving the stochastic fractional Volterra integro-differential equations of Hammerstein type	3
Recovering a space-dependent source term for distributed order time-space fractional diffusion equation	3
Fast and accurate numerical algorithm for solving stochastic Itô-Volterra integral equations	3
Flipped structured matrix-sequences in image deblurring with reflective and anti-reflective boundary conditions	3
Discrete non-commutative hungry Toda lattice and its application in matrix computation	3
The constant solution method for solving large-scale differential Sylvester matrix equations with time invariant coefficients	3
An efficient class of Traub-Steffensen-type optimal order multiple root solvers	3