Numerical Algorithms

Article	Citations
Fast solution method and simulation for the 2D time-space fractional Black-Scholes equation governing European two-asset option pricing	47
Uniformly accurate nested Picard iterative integrators for the Klein-Gordon-Schrödinger equation in the nonrelativistic regime	44
The backward rounding error analysis of the quaternion Givens QR decomposition	40
Optimal polynomial approximation to rational matrix functions using the Arnoldi algorithm	32
Correction to: Fitted schemes for Caputo-Hadamard fractional differential equations	27
A unified convergence analysis of the derivative-free projection-based method for constrained nonlinear monotone equations	24
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	21
The application of Goeken–Johnson’s Runge–Kutta methods in unconstrained convex optimization	21
Balanced-norm error estimate of the local discontinuous Galerkin method on layer-adapted meshes for reaction-diffusion problems	20
Numerical analysis of a linearly backward Euler method with truncated Wiener process for a stochastic SIS model	20
Modified globally convergent Polak-Ribière-Polyak conjugate gradient methods with self-correcting property for large-scale unconstrained optimization	20
Reducing swamp behavior for the canonical polyadic decomposition problem by rank-1 freezing	20
The linear barycentric rational backward differentiation formulae for stiff ODEs on nonuniform grids	20
Convergence, weak w2 stability, and data dependence results for the F iterative scheme in hyperbolic spaces	19
Local and parallel finite element methods based on two-grid discretizations for the unsteady mixed Stokes-Darcy model with the Beavers-Joseph interface condition	19
Modulus-based synchronous multisplitting iteration methods for large sparse vertical linear complementarity problems	19
Several accelerated subspace minimization conjugate gradient methods based on regularization model and convergence rate analysis for nonconvex problems	18
New modulus-based matrix splitting methods for implicit complementarity problem	16
Positive quadrature formulas on an arc of the unit circle	16
Krylov iterative methods for linear least squares problems with linear equality constraints	16
A multipoint flux mixed finite element method with mass-conservative characteristic finite element method for incompressible miscible displacement problem	15
On a class of infinite M-matrices with an extended quasi-Toeplitz structure	15
TRIPs-Py: Techniques for regularization of inverse problems in python	15
Interlacing and bounds of zeros of quasi-orthogonal little q-Jacobi polynomials	15

Implementation of divided differences to shape preservation	15
On the dynamics of Steffensen’s family of root-finding methods for entire function	15
High accuracy two-level compact implicit method in exponential form for 2D fourth order quasi-linear parabolic equations	14
Fourier transforms of orthogonal polynomials on the cone	14
High modes smoothing of time schemes for nonlinear parabolic PDEs	14
A novel banded preconditioner for coupled tempered fractional diffusion equation generated from the regime-switching CGMY model	14
Regularized Barzilai-Borwein Method	14
Solving non-differentiable Hammerstein integral equations via first-order divided differences	14
Extrapolation quadrature from equispaced samples of functions with jumps	14
Weak convergence of Euler scheme for SDEs with low regular drift	14
A simple yet efficient two-step fifth-order weighted-Newton method for nonlinear models	13
Decompose-then-optimize: a new approach to design domain decomposition methods for optimal control problems	13
Maximal residual coordinate descent method with k-means clustering for solving large linear least-squares problems	13
Orthogonal Cauchy-like matrices	13
Banded preconditioning with shift compensation for solving discrete Riesz space-fractional diffusion equations	13
A mixed precision LOBPCG algorithm	13
Multivariate polynomial interpolation based on Radon projections	12
Randomized flexible GMRES with deflated restarting	12
A modulus-based cascadic multigrid method for elliptic variational inequality problems	12
Improvements to steepest descent method for multi-objective optimization	12
Modulus-based block triangular splitting iteration method for solving the generalized absolute value equations	12
On the maximal order of convergence of Green’s function method for solving two-point boundary value problems with deviating argument	12
Correction to: “Patch area and uniform sampling on the surface of any ellipsoid”	11
Shift-splitting fixed point iteration method for solving generalized absolute value equations	11
Comments on “Fractal functions associated with Reich contractions: an approximation of chaotic attractors”	11
Greedy adaptive local recovery of functions in Sobolev spaces	11
On the accurate computation of the Newton form of the Lagrange interpolant	11
A class of new three-term descent conjugate gradient algorithms for large-scale unconstrained optimization and applications to image restoration problems	11
A spatial branch and bound algorithm for solving the sum of linear ratios optimization problem	11
A numerical method based on Legendre wavelet and quasilinearization technique for fractional Lane-Emden type equations	11
Szegő quadrature formulas associated with the weight function $$1+\cos (m\theta )$$ with application to the approximation of certain Christoffel transformations on the interval	11
Numerical solution to the exterior Bernoulli problem using the Dirichlet-Robin energy gap cost functional approach in two and three dimensions	11
First order strong approximation of Ait–Sahalia-type interest rate model with Poisson jumps	11
Total positivity and accurate computations with Gram matrices of Bernstein bases	11
A family of gradient methods using Householder transformation with application to hypergraph partitioning	10
Global convergence of a spectral conjugate gradient method for unconstrained optimization	10
Logarithmic function minimization to compressed sensing with application to magnetic resonance imaging	10
Complex moment-based methods for differential eigenvalue problems	10
Solving semi-discrete optimal transport problems: star shapedeness and Newton’s method	10
Communication in multiplex transportation networks	10
Local and parallel stabilized finite element methods based on two-grid discretizations for the Stokes equations	10
A multidimensional Hermite-Gauss sampling formula for analytic functions of several variables	10
Preconditioned inexact fixed point iteration method for solving tensor absolute value equation	10
Analysis of the basins of attraction generated by a pseudo Newton-Raphson method iterating over complex order derivatives	10
Incomplete double-cone factorizations of centrosymmetric matrices arising in spectral methods	10
Proximal variable smoothing method for three-composite nonconvex nonsmooth minimization with a linear operator	10
Applications of quasideterminants to non-commutative multistep $$\varepsilon $$-algorithm	9
Optimal Control problems of NS-$$\alpha $$ and NS-$$\omega $$ turbulence models: analysis and numerical tests	9
A fast second-order predictor-corrector method for a nonlinear time-fractional Benjamin-Bona-Mahony-Burgers equation	9
Linear and nonlinear substructured Restricted Additive Schwarz iterations and preconditioning	9

Polynomial estimates for the method of cyclic projections in Hilbert spaces	9
Higher-order recurrence relations, Sobolev-type inner products and matrix factorizations	9
Vem++, a C++ library to handle and play with the virtual element method	9
Optimal error estimate of the penalty method for the 2D/3D time-dependent MHD equations	9
Optimized Schwarz domain decomposition algorithms for the closest point method on closed manifolds	9
Adaptive cross approximation for Tikhonov regularization in general form	9
Maximum bound principle for matrix-valued Allen-Cahn equation and integrating factor Runge-Kutta method	9
A non-linear conjugate gradient in dual space for $$L_p$$-norm regularized non-linear least squares with application in data assimilation	8
Integrable semi-discretizations and self-adaptive moving mesh method for a generalized sine-Gordon equation	8
Interpolation preservation of AMF-W methods for linear diffusion problems	8
Comprehensive deep contrastive manifold regularized non-negative matrix factorization for multi-view clustering	8
Accurate inverses and determinants of doubly strictly diagonally dominant Z-matrices	8
Exact subdomain and embedded interface polynomial integration in finite elements with planar cuts	8
Alternated inertial algorithms for split feasibility problems	8
Computing Gaussian quadrature rules with high relative accuracy	8
Averaged cubature schemes on the real positive semiaxis	8
A robust variant of cubic smoothing spline approximation	8
Inertial Bregman proximal gradient under partial smoothness	8
Constructing Sobolev orthonormal rational functions via an updating procedure	8
A solely time-dependent source reconstruction in a multiterm time-fractional order diffusion equation with non-smooth solutions	8
Smaller stencil preconditioners for linear systems in RBF-FD discretizations	8
A new modified Mann-type method for solving the monotone inclusion problem and the fixed point problem in reflexive Banach spaces	8
Extended explicit Pseudo two-step Runge-Kutta-Nyström methods for general second-order oscillatory systems	8
Fitted schemes for Caputo-Hadamard fractional differential equations	8
Correction to: High-order linearly implicit exponential integrators conserving quadratic invariants with application to scalar auxiliary variable approach	8
Legendre polynomial based approximation of the Hessian for quasi-Newton optimization	8
Fractional-order Chelyshkov wavelet method for solving variable-order fractional differential equations and an application in variable-order fractional relaxation system	8
Non-linear WENO B-spline based approximation method	8
Hybrid coupling of finite element and boundary element methods using Nitsche’s method and the Calderon projection	8
A two-grid combined mixed finite element and discontinuous Galerkin method for a compressible miscible displacement problem	8
Fast superconvergent solvers for weakly singular Hammerstein equations	7
A new family of fourth-order energy-preserving integrators	7
Accuracy and stability of the column pivoting quaternion Householder QR factorization	7
Analysis of a higher-order scheme for multi-term time-fractional integro-partial differential equations with multi-term weakly singular kernels	7
A fault detection method based on partition of unity and kernel approximation	7
An incomplete tridiagonalization-based determinant evaluation for a generalized periodic tridiagonal matrix	7
A variational regularization method for solving the non-characteristic Cauchy problem in multiple dimensions	7
Sliding modes of high codimension in piecewise-smooth dynamical systems	7
Runge–Kutta methods determined from extended phase space methods for Hamiltonian systems	7
Fractional Legendre wavelet approach resolving multi-scale optimal control problems involving Caputo-Fabrizio derivative	7
The truncated Euler-Maruyama method for highly nonlinear stochastic differential equations with multiple time delays	7
The behavior of the Gauss-Radau upper bound of the error norm in CG	7
An MP-DWR method for h-adaptive finite element methods	7
Fully numerical Laplace transform methods	7
Unconditionally positivity-preserving approximations of the Aït-Sahalia type model: Explicit Milstein-type schemes	7
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 problem	7
A new approach of shifted Jacobi spectral Galerkin methods (SJSGM) for weakly singular Fredholm integral equation with non-smooth solution	7
H-representation method for the least squares symmetric solutions of the reduced biquaternion matrix equation and its application in color image restoration	7
Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the third and fourth kinds	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
Non-blind constraint image deblurring problem with mean curvature functional	7
Stochastic incremental mirror descent algorithms with Nesterov smoothing	7
A new optimal root-finding iterative algorithm: local and semilocal analysis with polynomiography	6
Tensor Interpolation	6
A cubic regularization of Newton’s method with finite difference Hessian approximations	6
Nonmonotone Quasi–Newton-based conjugate gradient methods with application to signal processing	6
An improved preconditioned inexact Uzawa method for elliptic optimal control problems	6
A mixed virtual element method for the time-fractional fourth-order subdiffusion equation	6
Generalized discrete Lotka-Volterra equation, orthogonal polynomials and generalized epsilon algorithm	6
Correction to: On the best achievable quality of limit points of augmented Lagrangian schemes	6
Another Hager-Zhang-type method via singular-value study for constrained monotone equations with application	6
TT-LSQR for tensor least squares problems and application to data mining	6
Boundary corrections on multi-dimensional PDEs	6
The generalized modular string averaging procedure and its applications to iterative methods for solving various nonlinear operator theory problems	6
A nonsmooth Newton method for solving the generalized complementarity problem	6
The method of randomized Bregman projections for stochastic feasibility problems	6
A hybrid gradient method for vector optimization problems	6
Explicit numerical methods for solving singular initial value problems for systems of second-order nonlinear ODEs	6
Revisiting the (block) Jacobi subspace rotation method for the symmetric eigenvalue problem	6
Stieltjes interlacing of zeros of little q-Jacobi and q-Laguerre polynomials from different sequences	6
An efficient numerical algorithm based on Haar wavelets for multi-dimensional nonlinear elliptic PDEs	6
Unconditionally energy stable IEQ-FEMs for the Cahn-Hilliard equation and Allen-Cahn equation	6
Optimal polynomial smoothers for parallel AMG	6
New proximal bundle algorithm based on the gradient sampling method for nonsmooth nonconvex optimization with exact and inexact information	6
A two-dimensional randomized extended Gauss-Seidel algorithm for solving least squares problems	6
Fast and accurate solvers for weakly singular integral equations	6
Optimal size of the block in block GMRES on GPUs: computational model and experiments	6
Limited memory gradient methods for unconstrained optimization	6

Fast and low-memory compressive sensing algorithms for low tucker-rank tensor approximation from streamed measurements	6
Inexact quasi-Newton methods under a relaxed metric regularity assumption	6
Fading regularization MFS algorithm for the Cauchy problem associated with the two-dimensional Stokes equations	6
Non-negative Einstein tensor factorization for unmixing hyperspectral images	6
On the randomized Euler schemes for ODEs under inexact information	6
Stochastic parareal algorithm for stochastic differential equations	6
Interpolated Galerkin finite elements on rectangular and cuboid meshes for the Poisson equation	6
On computing the zeros of a class of Sobolev orthogonal polynomials	6
Source-to-sink communicability: a new centrality measure for directed acyclic networks	6
A Numerical Approach for the System of Nonlinear Variable-order Fractional Volterra Integral Equations	6
Artificial compressibility SAV ensemble algorithms for the incompressible Navier-Stokes equations	5
Divergence of the Euler-Maruyama method for neutral stochastic differential equations with unbounded delay and Markovian switching	5
Two-level methods for solving higher order finite element discretizations of nonsymmetric and indefinite elliptic problem	5
A novel numerical scheme for time-fractional Black-Scholes PDE governing European options in mathematical finance	5
An effective computational approach based on new multi-step collocation method for solving integral-algebraic equations	5
Global convergence of a curvilinear search for non-convex optimization	5
Error bounds for the linear complementarity problems of $$N_1$$-matrices and $$BN_1$$-matrices	5
On the non-global linear stability and spurious fixed points of MPRK schemes with negative RK parameters	5
A weak Galerkin finite element method for singularly perturbed problems with two small parameters on Bakhvalov-type meshes	5
Mixed noise removal via generalized gaussian scale mixture modeling and plug-and-play deep prior	5
An inexact proximal majorization-minimization algorithm for remote sensing image stripe noise removal	5
A fast second-order scheme for nonlinear Riesz space-fractional diffusion equations	5
A class of modified accelerated proximal gradient methods for nonsmooth and nonconvex minimization problems	5
Acceleration of sequences with transformations involving hypergeometric functions	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
Hermite interpolation theorems for band-limited functions of the linear canonical transforms with equidistant samples	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
On the convergence of two-step modified Newton method for nonsymmetric algebraic Riccati equations from transport theory	5
The global convergence of the BFGS method with a modified WWP line search for nonconvex functions	5
Estimating error norms in CG-like algorithms for least-squares and least-norm problems	5
A fourth-order collocation scheme for generalized Black-Scholes model in financial decision-making	5
Strong convergence and extinction of positivity preserving explicit scheme for the stochastic SIS epidemic model	5
A high-order numerical scheme and its analysis for Caputo temporal-fractional Black-Scholes model: European double barrier knock-out option	5
Cut-edge centralities in an undirected graph	5
Quantifying mixing in arbitrary fluid domains: a Padé approximation approach	5
Finite element approximation of optimal control problem with integral fractional Laplacian and state constraint	5
A closest point method library for PDEs on surfaces with parallel domain decomposition solvers and preconditioners	5
A fast algorithm for time-fractional diffusion equation with space-time-dependent variable order	5
Fast and stable rational approximation of generalized hypergeometric functions	5
Fractal interpolation on the real projective plane	5
A hybrid-inertial accelerated spectral CG projection method with restart mechanism and its application to compressed sensing	5
A projection algorithm for pseudomonotone vector fields with convex constraints on Hadamard manifolds	5
Deviation maximization for rank-revealing QR factorizations	5
On estimating the separation associated with the periodic continuous Sylvester equation	5
Max-convolution through numerics and tropical geometry	5
Adaptive time step selection for spectral deferred correction	5
Some combined techniques of spectral conjugate gradient methods with applications to robotic and image restoration models	5
A conformable fractional iterative fixed-point method for solving one-dimensional nonlinear equations	5
Role extraction by matrix equations and generalized random walks	5
Reducing the truncation error in Taylor model multiplication	5
Equivalence and convergence analysis of fixed point iterative schemes using higher order averaged mappings	5
On Hölder global optimization method using piecewise affine bounding functions	5
A fast stable accurate artificial boundary condition for the linearized Green-Naghdi system	5
A note on the Grcar matrix	5
Enhancing image restoration using a discrete variational model with triangular mesh-based TV	4
A family of optimal weighted conjugate-gradient-type methods for strictly convex quadratic minimization	4
Modified Newton-PBS method for solving a class of complex symmetric nonlinear systems	4
Compact finite difference schemes and error estimation for third-order Emden-Fowler equations	4
Analytical and numerical studies of the modified Kawahara equation with dual-power law nonlinearities	4
HODLR3D: hierarchical matrices for N-body problems in three dimensions	4
Another HSS iteration method	4
Lagrange interpolation polynomials for solving nonlinear stochastic integral equations	4
Variable parameter Uzawa method for solving the indefinite least squares problem	4
Modified projection method and strong convergence theorem for solving variational inequality problems with non-Lipschitz operators	4
Inertial self-adaptive algorithms for solving non-smooth convex optimization problems	4
Optimality and duality results for fractional programming problems under E-univexity	4
Discrete mollification in Bernstein basis and space marching scheme for numerical solution of an inverse two-phase one-dimensional Stefan problem	4
A new algorithm for solving a class of matrix optimization problem arising in unsupervised feature selection	4
Improved Gegenbauer spectral tau algorithms for distributed-order time-fractional telegraph models in multi-dimensions	4
Approximate linearization of fixed-point iterations	4
Boundary reconstruction in two-dimensional steady-state anisotropic heat conduction	4
Two-point Padé approximation to Herglotz-Riesz transforms	4
On the convergence of Galerkin methods for auto-convolution Volterra integro-differential equations	4
Edge importance in complex networks	4
On multivariate orthogonal polynomials and elementary symmetric functions	4
Two new self-adaptive algorithms for solving the split feasibility problem in Hilbert space	4
The semi-implicit DLN algorithm for the Navier-Stokes equations	4
Numerical solution of the boundary value problems for the biharmonic equations via quasiseparable representations	4
Operator-splitting finite element method for solving the radiative transfer equation	4
On the computation of the cumulative distribution function of the normal inverse Gaussian distribution	4
The explicit form of the vector $$\varepsilon $$-algorithm’s kernel : a conjecture and its solution in $$\mathbb {R}^4 $$	4
Adaptive multiplication of $$\mathcal {H}^2$$-matrices with block-relative error control	4
High-order $$L^{2}$$-bound-preserving Fourier pseudo-spectral schemes for the Allen-Cahn equation	4
Globally convergent diagonal Polak–Ribière–Polyak like algorithm for nonlinear equations	4
Numerical solution of distributed-order fractional Korteweg-de Vries equation via fractional Zigzag rising diagonal functions	4
Correction to: fast and accurate numerical algorithm for solving stochastic itô-volterra integral equations	4
A third-order iterative algorithm for inversion of cumulative central beta distribution	4
An efficient fractional step numerical algorithm for time-delayed singularly perturbed 2D convection-diffusion–reaction problem with two small parameters	4
A novel high-order numerical scheme and its analysis for the two-dimensional time-fractional reaction-subdiffusion equation	4
C-FISTA type projection algorithm for quasi-variational inequalities	4
A second-order BDF convex splitting numerical scheme for the Ericksen-Leslie equation	4
Approximation operators explored through the lens of degenerate hermite polynomials	4
The quaternion relaxed greedy randomized Kaczmarz method with adaptive parameters for solving quaternion matrix equation	4
Network analysis with the aid of the path length matrix	4