Numerical Algorithms

Article	Citations
Fast solution method and simulation for the 2D time-space fractional Black-Scholes equation governing European two-asset option pricing	49
Uniformly accurate nested Picard iterative integrators for the Klein-Gordon-Schrödinger equation in the nonrelativistic regime	45
ENO-based high-order data-bounded and constrained positivity-preserving interpolation	41
Correction to: Fitted schemes for Caputo-Hadamard fractional differential equations	36
The application of Goeken–Johnson’s Runge–Kutta methods in unconstrained convex optimization	27
The linear barycentric rational backward differentiation formulae for stiff ODEs on nonuniform grids	24
The backward rounding error analysis of the quaternion Givens QR decomposition	22
Reducing swamp behavior for the canonical polyadic decomposition problem by rank-1 freezing	22
Two novel numerical methods for gradient flows: generalizations of the Invariant Energy Quadratization method	22
TRIPs-Py: Techniques for regularization of inverse problems in python	21
A unified convergence analysis of the derivative-free projection-based method for constrained nonlinear monotone equations	21
Krylov iterative methods for linear least squares problems with linear equality constraints	20
Several accelerated subspace minimization conjugate gradient methods based on regularization model and convergence rate analysis for nonconvex problems	20
Implementation of divided differences to shape preservation	20
Local and parallel finite element methods based on two-grid discretizations for the unsteady mixed Stokes-Darcy model with the Beavers-Joseph interface condition	20
A multipoint flux mixed finite element method with mass-conservative characteristic finite element method for incompressible miscible displacement problem	19
Positive quadrature formulas on an arc of the unit circle	19
On the dynamics of Steffensen’s family of root-finding methods for entire function	19
Modified globally convergent Polak-Ribière-Polyak conjugate gradient methods with self-correcting property for large-scale unconstrained optimization	18
Convergence, weak w2 stability, and data dependence results for the F iterative scheme in hyperbolic spaces	17
Optimal polynomial approximation to rational matrix functions using the Arnoldi algorithm	17
New modulus-based matrix splitting methods for implicit complementarity problem	16
Numerical analysis of a linearly backward Euler method with truncated Wiener process for a stochastic SIS model	16
Convergence properties of a new projection algorithm for pseudomonotone vector fields on hadamard manifolds	15
A class of new three-term descent conjugate gradient algorithms for large-scale unconstrained optimization and applications to image restoration problems	15

Interlacing and bounds of zeros of quasi-orthogonal little q-Jacobi polynomials	15
Modulus-based synchronous multisplitting iteration methods for large sparse vertical linear complementarity problems	15
Correction to: “Patch area and uniform sampling on the surface of any ellipsoid”	15
Balanced-norm error estimate of the local discontinuous Galerkin method on layer-adapted meshes for reaction-diffusion problems	15
High modes smoothing of time schemes for nonlinear parabolic PDEs	15
A simple yet efficient two-step fifth-order weighted-Newton method for nonlinear models	15
Szegő quadrature formulas associated with the weight function $$1+\cos (m\theta )$$ with application to the approximation of certain Christoffel transformations on the interval	14
A modulus-based cascadic multigrid method for elliptic variational inequality problems	14
Solving non-differentiable Hammerstein integral equations via first-order divided differences	14
A novel banded preconditioner for coupled tempered fractional diffusion equation generated from the regime-switching CGMY model	14
Numerical solution to the exterior Bernoulli problem using the Dirichlet-Robin energy gap cost functional approach in two and three dimensions	14
Extrapolation quadrature from equispaced samples of functions with jumps	14
Fourier transforms of orthogonal polynomials on the cone	14
Multivariate polynomial interpolation based on Radon projections	14
On a class of infinite M-matrices with an extended quasi-Toeplitz structure	14
Regularized Barzilai-Borwein Method	14
Banded preconditioning with shift compensation for solving discrete Riesz space-fractional diffusion equations	13
Modulus-based block triangular splitting iteration method for solving the generalized absolute value equations	13
Decompose-then-optimize: a new approach to design domain decomposition methods for optimal control problems	13
On the maximal order of convergence of Green’s function method for solving two-point boundary value problems with deviating argument	13
Maximal residual coordinate descent method with k-means clustering for solving large linear least-squares problems	13
Improvements to steepest descent method for multi-objective optimization	12
A mixed precision LOBPCG algorithm	12
Randomized flexible GMRES with deflated restarting	12
High accuracy two-level compact implicit method in exponential form for 2D fourth order quasi-linear parabolic equations	12
Orthogonal Cauchy-like matrices	12
Logarithmic function minimization to compressed sensing with application to magnetic resonance imaging	11
Interpolated Galerkin finite elements on triangular meshes for the biharmonic equation	11
Shift-splitting fixed point iteration method for solving generalized absolute value equations	11
Incomplete double-cone factorizations of centrosymmetric matrices arising in spectral methods	11
Complex moment-based methods for differential eigenvalue problems	11
A spatial branch and bound algorithm for solving the sum of linear ratios optimization problem	11
Higher-order recurrence relations, Sobolev-type inner products and matrix factorizations	11
A multidimensional Hermite-Gauss sampling formula for analytic functions of several variables	11
Total positivity and accurate computations with Gram matrices of Bernstein bases	11
On the accurate computation of the Newton form of the Lagrange interpolant	11
Solving semi-discrete optimal transport problems: star shapedeness and Newton’s method	11
Fitted schemes for Caputo-Hadamard fractional differential equations	10
Greedy adaptive local recovery of functions in Sobolev spaces	10
Vem++, a C++ library to handle and play with the virtual element method	10
Optimal error estimate of the penalty method for the 2D/3D time-dependent MHD equations	10
Inertial subgradient splitting projection methods for solving equilibrium problems and applications	10
Optimized Schwarz domain decomposition algorithms for the closest point method on closed manifolds	10
Preconditioned inexact fixed point iteration method for solving tensor absolute value equation	10
Fractional-order Chelyshkov wavelet method for solving variable-order fractional differential equations and an application in variable-order fractional relaxation system	10
A family of gradient methods using Householder transformation with application to hypergraph partitioning	10
Communication in multiplex transportation networks	10
A numerical method based on Legendre wavelet and quasilinearization technique for fractional Lane-Emden type equations	10
Analysis of the basins of attraction generated by a pseudo Newton-Raphson method iterating over complex order derivatives	10
Linear and nonlinear substructured Restricted Additive Schwarz iterations and preconditioning	9

Proximal variable smoothing method for three-composite nonconvex nonsmooth minimization with a linear operator	9
Adaptive cross approximation for Tikhonov regularization in general form	9
First order strong approximation of Ait–Sahalia-type interest rate model with Poisson jumps	9
Local and parallel stabilized finite element methods based on two-grid discretizations for the Stokes equations	9
Maximum bound principle for matrix-valued Allen-Cahn equation and integrating factor Runge-Kutta method	9
A fast second-order predictor-corrector method for a nonlinear time-fractional Benjamin-Bona-Mahony-Burgers equation	9
Comments on “Fractal functions associated with Reich contractions: an approximation of chaotic attractors”	9
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
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
Extended explicit Pseudo two-step Runge-Kutta-Nyström methods for general second-order oscillatory systems	8
Alternated inertial algorithms for split feasibility problems	8
Inertial Bregman proximal gradient under partial smoothness	8
Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the third and fourth kinds	8
A new modified Mann-type method for solving the monotone inclusion problem and the fixed point problem in reflexive Banach spaces	8
A robust variant of cubic smoothing spline approximation	8
Hybrid coupling of finite element and boundary element methods using Nitsche’s method and the Calderon projection	8
A new approach of shifted Jacobi spectral Galerkin methods (SJSGM) for weakly singular Fredholm integral equation with non-smooth solution	8
Correction to: High-order linearly implicit exponential integrators conserving quadratic invariants with application to scalar auxiliary variable approach	8
Deep learning, transformers and graph neural networks: a linear algebra perspective	8
Comprehensive deep contrastive manifold regularized non-negative matrix factorization for multi-view clustering	8
Integrable semi-discretizations and self-adaptive moving mesh method for a generalized sine-Gordon equation	8
A two-grid combined mixed finite element and discontinuous Galerkin method for a compressible miscible displacement problem	8
A non-linear conjugate gradient in dual space for $$L_p$$-norm regularized non-linear least squares with application in data assimilation	8
Interpolation preservation of AMF-W methods for linear diffusion problems	8
Legendre polynomial based approximation of the Hessian for quasi-Newton optimization	8
Constructing Sobolev orthonormal rational functions via an updating procedure	8
Non-linear WENO B-spline based approximation method	8
Exact subdomain and embedded interface polynomial integration in finite elements with planar cuts	8
The truncated Euler-Maruyama method for highly nonlinear stochastic differential equations with multiple time delays	8
A stable second-order difference scheme for the generalized time-fractional non-Fickian delay reaction-diffusion equations	7
A new family of fourth-order energy-preserving integrators	7
Computing Gaussian quadrature rules with high relative accuracy	7
Accuracy and stability of the column pivoting quaternion Householder QR factorization	7
Locally conservative discontinuous bubble scheme for Darcy flow and its application to Hele-Shaw equation based on structured grids	7
Fast superconvergent solvers for weakly singular Hammerstein equations	7
Nonmonotone Quasi–Newton-based conjugate gradient methods with application to signal processing	7
An MP-DWR method for h-adaptive finite element methods	7
A fault detection method based on partition of unity and kernel approximation	7
A three-step modulus-based iterative method for solving nonlinear complementarity problems	7
Smaller stencil preconditioners for linear systems in RBF-FD discretizations	7
Analysis of a higher-order scheme for multi-term time-fractional integro-partial differential equations with multi-term weakly singular kernels	7
A variational regularization method for solving the non-characteristic Cauchy problem in multiple dimensions	7
Stochastic parareal algorithm for stochastic differential equations	7
Stochastic incremental mirror descent algorithms with Nesterov smoothing	7
Generalized discrete Lotka-Volterra equation, orthogonal polynomials and generalized epsilon algorithm	7
H-representation method for the least squares symmetric solutions of the reduced biquaternion matrix equation and its application in color image restoration	7
Accurate inverses and determinants of doubly strictly diagonally dominant Z-matrices	7
Fractional Legendre wavelet approach resolving multi-scale optimal control problems involving Caputo-Fabrizio derivative	7
Sliding modes of high codimension in piecewise-smooth dynamical systems	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
Correction to: On the best achievable quality of limit points of augmented Lagrangian schemes	7
Non-blind constraint image deblurring problem with mean curvature functional	7
Fully numerical Laplace transform methods	7
Tensor Interpolation	6
On the randomized Euler schemes for ODEs under inexact information	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
An efficient numerical algorithm based on Haar wavelets for multi-dimensional nonlinear elliptic PDEs	6
Fast and low-memory compressive sensing algorithms for low tucker-rank tensor approximation from streamed measurements	6
TT-LSQR for tensor least squares problems and application to data mining	6
Adaptive time step selection for spectral deferred correction	6
Estimating error norms in CG-like algorithms for least-squares and least-norm problems	6
Fading regularization MFS algorithm for the Cauchy problem associated with the two-dimensional Stokes equations	6
Fast and accurate solvers for weakly singular integral equations	6
Source-to-sink communicability: a new centrality measure for directed acyclic networks	6
Another Hager-Zhang-type method via singular-value study for constrained monotone equations with application	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
Runge–Kutta methods determined from extended phase space methods for Hamiltonian systems	6
The behavior of the Gauss-Radau upper bound of the error norm in CG	6
The method of randomized Bregman projections for stochastic feasibility problems	6
Interpolated Galerkin finite elements on rectangular and cuboid meshes for the Poisson equation	6
Error bounds for the linear complementarity problems of $$N_1$$-matrices and $$BN_1$$-matrices	6
A new optimal root-finding iterative algorithm: local and semilocal analysis with polynomiography	6
A nonsmooth Newton method for solving the generalized complementarity problem	6
Optimal polynomial smoothers for parallel AMG	6
A Numerical Approach for the System of Nonlinear Variable-order Fractional Volterra Integral Equations	6

A hybrid gradient method for vector optimization problems	6
Boundary corrections on multi-dimensional PDEs	6
Non-negative Einstein tensor factorization for unmixing hyperspectral images	6
Unconditionally energy stable IEQ-FEMs for the Cahn-Hilliard equation and Allen-Cahn equation	6
Piecewise numerical approach for solving piecewise fractional optimal control and variational problems	6
Limited memory gradient methods for unconstrained optimization	6
The generalized modular string averaging procedure and its applications to iterative methods for solving various nonlinear operator theory problems	6
A two-dimensional randomized extended Gauss-Seidel algorithm for solving least squares problems	6
A fourth-order collocation scheme for generalized Black-Scholes model in financial decision-making	6
Optimal size of the block in block GMRES on GPUs: computational model and experiments	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
On computing the zeros of a class of Sobolev orthogonal polynomials	6
Stieltjes interlacing of zeros of little q-Jacobi and q-Laguerre polynomials from different sequences	5
Inexact quasi-Newton methods under a relaxed metric regularity assumption	5
Fractal interpolation on the real projective plane	5
New structure-preserving algorithms of Gauss-Seidel and successive over-relaxation iteration methods for quaternion linear systems	5
Cut-edge centralities in an undirected graph	5
On Hölder global optimization method using piecewise affine bounding functions	5
Reducing the truncation error in Taylor model multiplication	5
A projection algorithm for pseudomonotone vector fields with convex constraints on Hadamard manifolds	5
A hybrid-inertial accelerated spectral CG projection method with restart mechanism and its application to compressed sensing	5
An effective computational approach based on new multi-step collocation method for solving integral-algebraic equations	5
A note on the Grcar matrix	5
A high-order numerical scheme and its analysis for Caputo temporal-fractional Black-Scholes model: European double barrier knock-out option	5
On estimating the separation associated with the periodic continuous Sylvester equation	5
Max-convolution through numerics and tropical geometry	5
A predictor-corrector finite element method for parabolic problems on polygonal domains	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 class of modified accelerated proximal gradient methods for nonsmooth and nonconvex minimization problems	5
Equivalence and convergence analysis of fixed point iterative schemes using higher order averaged mappings	5
An inexact proximal majorization-minimization algorithm for remote sensing image stripe noise removal	5
Acceleration of sequences with transformations involving hypergeometric functions	5
Some combined techniques of spectral conjugate gradient methods with applications to robotic and image restoration models	5
A fast second-order scheme for nonlinear Riesz space-fractional diffusion equations	5
Two new self-adaptive algorithms for solving the split feasibility problem in Hilbert space	5
Divergence of the Euler-Maruyama method for neutral stochastic differential equations with unbounded delay and Markovian switching	5
The global convergence of the BFGS method with a modified WWP line search for nonconvex functions	5
Artificial compressibility SAV ensemble algorithms for the incompressible Navier-Stokes equations	5
Quantifying mixing in arbitrary fluid domains: a Padé approximation approach	5
A conformable fractional iterative fixed-point method for solving one-dimensional nonlinear equations	5
Global convergence of a curvilinear search for non-convex optimization	5
New proximal bundle algorithm based on the gradient sampling method for nonsmooth nonconvex optimization with exact and inexact information	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
$$O(1/k^2)$$ convergence rates of (dual-primal) balanced augmented Lagrangian methods for linearly constrained convex programming	5
Finite element approximation of optimal control problem with integral fractional Laplacian and state constraint	5
Fast and stable rational approximation of generalized hypergeometric functions	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 fast stable accurate artificial boundary condition for the linearized Green-Naghdi system	5
Refined and refined harmonic Jacobi–Davidson methods for computing several GSVD components of a large regular matrix pair	5
Strong convergence and extinction of positivity preserving explicit scheme for the stochastic SIS epidemic model	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
On the convergence of two-step modified Newton method for nonsymmetric algebraic Riccati equations from transport theory	5
Discrete mollification in Bernstein basis and space marching scheme for numerical solution of an inverse two-phase one-dimensional Stefan problem	4
Approximate linearization of fixed-point iterations	4
Globally convergent diagonal Polak–Ribière–Polyak like algorithm for nonlinear equations	4
Another HSS iteration method	4
RMPIA: a new algorithm for computing the Lagrange matrix interpolation polynomials	4
A third-order iterative algorithm for inversion of cumulative central beta distribution	4
Role extraction by matrix equations and generalized random walks	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
On the convergence of Galerkin methods for auto-convolution Volterra integro-differential equations	4
Inertial self-adaptive algorithms for solving non-smooth convex optimization problems	4
Forward-reflected-backward algorithms with double inertial extrapolations for variational inequalities with applications to image processing	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
HODLR3D: hierarchical matrices for N-body problems in three dimensions	4
Several accelerated gradient-based iteration methods for solving $$AXB=C$$ with application to tensor surface fitting	4
The explicit form of the vector $$\varepsilon $$-algorithm’s kernel : a conjecture and its solution in $$\mathbb {R}^4 $$	4
A highly efficient class of optimal fourth-order methods for solving nonlinear systems	4
Approximation operators explored through the lens of degenerate hermite polynomials	4
Lagrange interpolation polynomials for solving nonlinear stochastic integral equations	4
On multivariate orthogonal polynomials and elementary symmetric functions	4
Fast Euler–Maruyama method for weakly singular stochastic Volterra integral equations with variable exponent	4
Variable parameter Uzawa method for solving the indefinite least squares problem	4
Boundary reconstruction in two-dimensional steady-state anisotropic heat conduction	4
A weak Galerkin pseudostress-based mixed finite element method on polygonal meshes: application to the Brinkman problem appearing in porous media	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
A second-order BDF convex splitting numerical scheme for the Ericksen-Leslie equation	4
Fractional centered difference schemes and banded preconditioners for nonlinear Riesz space variable-order fractional diffusion equations	4
Mixed noise removal via generalized gaussian scale mixture modeling and plug-and-play deep prior	4
Network analysis with the aid of the path length matrix	4
An efficient fractional step numerical algorithm for time-delayed singularly perturbed 2D convection-diffusion–reaction problem with two small parameters	4
Structure-preserving doubling algorithm for a quadratic matrix equation arising in noisy Markov chains	4
Enhancing image restoration using a discrete variational model with triangular mesh-based TV	4
Relaxed Tseng splitting method with double inertial steps for solving monotone inclusions and fixed point problems	4
Compact finite difference schemes and error estimation for third-order Emden-Fowler equations	4
Numerical solution of the boundary value problems for the biharmonic equations via quasiseparable representations	4
Explicit representations of the norms of the Laguerre-Sobolev and Jacobi-Sobolev polynomials	4
A new algorithm for solving a class of matrix optimization problem arising in unsupervised feature selection	4