Numerical Algorithms

Article	Citations
Fast solution method and simulation for the 2D time-space fractional Black-Scholes equation governing European two-asset option pricing	54
Uniformly accurate nested Picard iterative integrators for the Klein-Gordon-Schrödinger equation in the nonrelativistic regime	47
ENO-based high-order data-bounded and constrained positivity-preserving interpolation	43
Correction to: Fitted schemes for Caputo-Hadamard fractional differential equations	40
The application of Goeken–Johnson’s Runge–Kutta methods in unconstrained convex optimization	27
Modulus-based synchronous multisplitting iteration methods for large sparse vertical linear complementarity problems	27
Two novel numerical methods for gradient flows: generalizations of the Invariant Energy Quadratization method	25
The backward rounding error analysis of the quaternion Givens QR decomposition	25
A unified convergence analysis of the derivative-free projection-based method for constrained nonlinear monotone equations	23
Several accelerated subspace minimization conjugate gradient methods based on regularization model and convergence rate analysis for nonconvex problems	22
Convergence properties of a new projection algorithm for pseudomonotone vector fields on hadamard manifolds	22
Krylov iterative methods for linear least squares problems with linear equality constraints	22
A multipoint flux mixed finite element method with mass-conservative characteristic finite element method for incompressible miscible displacement problem	22
Implementation of divided differences to shape preservation	22
Convergence, weak w2 stability, and data dependence results for the F iterative scheme in hyperbolic spaces	21
Positive quadrature formulas on an arc of the unit circle	21
Modified globally convergent Polak-Ribière-Polyak conjugate gradient methods with self-correcting property for large-scale unconstrained optimization	21
TRIPs-Py: Techniques for regularization of inverse problems in python	19
Reducing swamp behavior for the canonical polyadic decomposition problem by rank-1 freezing	19
A nondeterministic branch-and-bound algorithm for maximizing the sum of a generalized Rayleigh quotient and a quadratic form on the unit sphere	18
Optimal polynomial approximation to rational matrix functions using the Arnoldi algorithm	18
On the dynamics of Steffensen’s family of root-finding methods for entire function	18
New modulus-based matrix splitting methods for implicit complementarity problem	17
Local and parallel finite element methods based on two-grid discretizations for the unsteady mixed Stokes-Darcy model with the Beavers-Joseph interface condition	17
New nonsingular H-matrix subclass with parameter-free infinity norm bounds and linear complementarity error estimates	16

Interlacing and bounds of zeros of quasi-orthogonal little q-Jacobi polynomials	16
Balanced-norm error estimate of the local discontinuous Galerkin method on layer-adapted meshes for reaction-diffusion problems	16
Numerical analysis of a linearly backward Euler method with truncated Wiener process for a stochastic SIS model	16
The linear barycentric rational backward differentiation formulae for stiff ODEs on nonuniform grids	16
High modes smoothing of time schemes for nonlinear parabolic PDEs	16
Szegő quadrature formulas associated with the weight function $$1+\cos (m\theta )$$ with application to the approximation of certain Christoffel transformations on the interval	15
Correction to: “Patch area and uniform sampling on the surface of any ellipsoid”	15
Multivariate polynomial interpolation based on Radon projections	15
A class of new three-term descent conjugate gradient algorithms for large-scale unconstrained optimization and applications to image restoration problems	15
A modulus-based cascadic multigrid method for elliptic variational inequality problems	15
Numerical solution to the exterior Bernoulli problem using the Dirichlet-Robin energy gap cost functional approach in two and three dimensions	15
On the accurate computation of the Newton form of the Lagrange interpolant	15
Decompose-then-optimize: a new approach to design domain decomposition methods for optimal control problems	14
Regularized Barzilai-Borwein Method	14
A novel banded preconditioner for coupled tempered fractional diffusion equation generated from the regime-switching CGMY model	14
A simple yet efficient two-step fifth-order weighted-Newton method for nonlinear models	14
Maximal residual coordinate descent method with k-means clustering for solving large linear least-squares problems	14
On a class of infinite M-matrices with an extended quasi-Toeplitz structure	14
Extrapolation quadrature from equispaced samples of functions with jumps	14
Shift-splitting fixed point iteration method for solving generalized absolute value equations	14
Modulus-based block triangular splitting iteration method for solving the generalized absolute value equations	14
Fourier transforms of orthogonal polynomials on the cone	14
Banded preconditioning with shift compensation for solving discrete Riesz space-fractional diffusion equations	14
Orthogonal Cauchy-like matrices	13
Randomized flexible GMRES with deflated restarting	13
Improvements to steepest descent method for multi-objective optimization	13
A spatial branch and bound algorithm for solving the sum of linear ratios optimization problem	13
A mixed precision LOBPCG algorithm	13
Solving non-differentiable Hammerstein integral equations via first-order divided differences	12
High accuracy two-level compact implicit method in exponential form for 2D fourth order quasi-linear parabolic equations	12
Average-based iterative methods for solving nonlinear integral equations and systems of ordinary equations	12
Interpolated Galerkin finite elements on triangular meshes for the biharmonic equation	12
On the maximal order of convergence of Green’s function method for solving two-point boundary value problems with deviating argument	12
Total positivity and accurate computations with Gram matrices of Bernstein bases	12
Solving semi-discrete optimal transport problems: star shapedeness and Newton’s method	11
Optimized Schwarz domain decomposition algorithms for the closest point method on closed manifolds	11
Greedy adaptive local recovery of functions in Sobolev spaces	11
Complex moment-based methods for differential eigenvalue problems	11
Higher-order recurrence relations, Sobolev-type inner products and matrix factorizations	11
Preconditioned inexact fixed point iteration method for solving tensor absolute value equation	11
Logarithmic function minimization to compressed sensing with application to magnetic resonance imaging	11
A multidimensional Hermite-Gauss sampling formula for analytic functions of several variables	11
Optimal error estimate of the penalty method for the 2D/3D time-dependent MHD equations	11
Polynomial estimates for the method of cyclic projections in Hilbert spaces	10
Optimal Control problems of NS-$$\alpha $$ and NS-$$\omega $$ turbulence models: analysis and numerical tests	10
Proximal variable smoothing method for three-composite nonconvex nonsmooth minimization with a linear operator	10
First order strong approximation of Ait–Sahalia-type interest rate model with Poisson jumps	10
General christoffel perturbations for multiple orthogonal polynomials of the mixed type on the step-line	10
Applications of quasideterminants to non-commutative multistep $$\varepsilon $$-algorithm	10
Maximum bound principle for matrix-valued Allen-Cahn equation and integrating factor Runge-Kutta method	10

Local and parallel stabilized finite element methods based on two-grid discretizations for the Stokes equations	10
Global convergence of a spectral conjugate gradient method for unconstrained optimization	10
Adaptive cross approximation for Tikhonov regularization in general form	10
Incomplete double-cone factorizations of centrosymmetric matrices arising in spectral methods	9
Analysis of the basins of attraction generated by a pseudo Newton-Raphson method iterating over complex order derivatives	9
Inertial subgradient splitting projection methods for solving equilibrium problems and applications	9
Vem++, a C++ library to handle and play with the virtual element method	9
Averaged cubature schemes on the real positive semiaxis	9
Iteration methods for the classical split quaternion tensor equation $$\mathcal {E}*_N\mathcal {X}*_N\mathcal {F}=\mathcal {D}$$	9
Fitted schemes for Caputo-Hadamard fractional differential equations	9
Communication in multiplex transportation networks	9
On unconditional stability of a penalty-based ensemble 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
A family of gradient methods using Householder transformation with application to hypergraph partitioning	9
Fractional-order Chelyshkov wavelet method for solving variable-order fractional differential equations and an application in variable-order fractional relaxation system	9
Linear and nonlinear substructured Restricted Additive Schwarz iterations and preconditioning	9
Extended explicit Pseudo two-step Runge-Kutta-Nyström methods for general second-order oscillatory systems	8
Integrable semi-discretizations and self-adaptive moving mesh method for a generalized sine-Gordon equation	8
A numerical method based on Legendre wavelet and quasilinearization technique for fractional Lane-Emden type 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
Alternated inertial algorithms for split feasibility problems	8
A robust variant of cubic smoothing spline approximation	8
Accuracy and stability of the column pivoting quaternion Householder QR factorization	8
A new approach of shifted Jacobi spectral Galerkin methods (SJSGM) for weakly singular Fredholm integral equation with non-smooth solution	8
A non-linear conjugate gradient in dual space for $$L_p$$-norm regularized non-linear least squares with application in data assimilation	8
Non-linear WENO B-spline based approximation method	8
The truncated Euler-Maruyama method for highly nonlinear stochastic differential equations with multiple time delays	8
Exact subdomain and embedded interface polynomial integration in finite elements with planar cuts	8
Deep learning, transformers and graph neural networks: a linear algebra perspective	8
A three-step modulus-based iterative method for solving nonlinear complementarity problems	8
Analysis of a higher-order scheme for multi-term time-fractional integro-partial differential equations with multi-term weakly singular kernels	8
Comprehensive deep contrastive manifold regularized non-negative matrix factorization for multi-view clustering	8
A new modified Mann-type method for solving the monotone inclusion problem and the fixed point problem in reflexive Banach spaces	8
Hybrid coupling of finite element and boundary element methods using Nitsche’s method and the Calderon projection	8
Interpolation preservation of AMF-W methods for linear diffusion problems	8
A two-grid combined mixed finite element and discontinuous Galerkin method for a compressible miscible displacement problem	8
Inertial Bregman proximal gradient under partial smoothness	8
Accurate inverses and determinants of doubly strictly diagonally dominant Z-matrices	8
Computing Gaussian quadrature rules with high relative accuracy	8
Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the third and fourth kinds	8
An incomplete tridiagonalization-based determinant evaluation for a generalized periodic tridiagonal matrix	7
Piecewise numerical approach for solving piecewise fractional optimal control and variational problems	7
Generalized discrete Lotka-Volterra equation, orthogonal polynomials and generalized epsilon algorithm	7
Stochastic incremental mirror descent algorithms with Nesterov smoothing	7
A modified spectral three-term hybrid derivative-free projection method using convex combination acceleration to solve nonlinear complementarity problems	7
Constructing Sobolev orthonormal rational functions via an updating procedure	7
Stochastic parareal algorithm for stochastic differential equations	7
A stable second-order difference scheme for the generalized time-fractional non-Fickian delay reaction-diffusion equations	7
Unconditionally energy stable IEQ-FEMs for the Cahn-Hilliard equation and Allen-Cahn equation	7
On the randomized Euler schemes for ODEs under inexact information	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
Fully numerical Laplace transform methods	7
A variational regularization method for solving the non-characteristic Cauchy problem in multiple dimensions	7
A new family of fourth-order energy-preserving integrators	7
Smaller stencil preconditioners for linear systems in RBF-FD discretizations	7
Sliding modes of high codimension in piecewise-smooth dynamical systems	7
The behavior of the Gauss-Radau upper bound of the error norm in CG	7
A mixed virtual element method for the time-fractional fourth-order subdiffusion equation	7
A fault detection method based on partition of unity and kernel approximation	7
Runge–Kutta methods determined from extended phase space methods for Hamiltonian systems	7
Non-blind constraint image deblurring problem with mean curvature functional	7
An MP-DWR method for h-adaptive finite element methods	7
Locally conservative discontinuous bubble scheme for Darcy flow and its application to Hele-Shaw equation based on structured grids	7
H-representation method for the least squares symmetric solutions of the reduced biquaternion matrix equation and its application in color image restoration	7
Fractional Legendre wavelet approach resolving multi-scale optimal control problems involving Caputo-Fabrizio derivative	7
Fast superconvergent solvers for weakly singular Hammerstein equations	7
Unconditionally positivity-preserving approximations of the Aït-Sahalia type model: Explicit Milstein-type schemes	7
Nonmonotone Quasi–Newton-based conjugate gradient methods with application to signal processing	7
An efficient numerical algorithm based on Haar wavelets for multi-dimensional nonlinear elliptic PDEs	7
Limited memory gradient methods for unconstrained optimization	6
Another Hager-Zhang-type method via singular-value study for constrained monotone equations with application	6
A new optimal root-finding iterative algorithm: local and semilocal analysis with polynomiography	6
The generalized modular string averaging procedure and its applications to iterative methods for solving various nonlinear operator theory problems	6
Source-to-sink communicability: a new centrality measure for directed acyclic networks	6
Revisiting the (block) Jacobi subspace rotation method for the symmetric eigenvalue problem	6
A Numerical Approach for the System of Nonlinear Variable-order Fractional Volterra Integral Equations	6
Optimal polynomial smoothers for parallel AMG	6
A nonsmooth Newton method for solving the generalized complementarity problem	6

Inexact quasi-Newton methods under a relaxed metric regularity assumption	6
On the convergence of two-step modified Newton method for nonsymmetric algebraic Riccati equations from transport theory	6
On estimating the separation associated with the periodic continuous Sylvester equation	6
The method of randomized Bregman projections for stochastic feasibility problems	6
Boundary corrections on multi-dimensional PDEs	6
Interpolated Galerkin finite elements on rectangular and cuboid meshes for the Poisson equation	6
New proximal bundle algorithm based on the gradient sampling method for nonsmooth nonconvex optimization with exact and inexact information	6
A predictor-corrector finite element method for parabolic problems on polygonal domains	6
A hybrid gradient method for vector optimization problems	6
Tensor Interpolation	6
Fast and low-memory compressive sensing algorithms for low tucker-rank tensor approximation from streamed measurements	6
Explicit numerical methods for solving singular initial value problems for systems of second-order nonlinear ODEs	6
A fourth-order collocation scheme for generalized Black-Scholes model in financial decision-making	6
Max-convolution through numerics and tropical geometry	6
Stieltjes interlacing of zeros of little q-Jacobi and q-Laguerre polynomials from different sequences	6
A conformable fractional iterative fixed-point method for solving one-dimensional nonlinear equations	6
Fading regularization MFS algorithm for the Cauchy problem associated with the two-dimensional Stokes equations	6
Error bounds for the linear complementarity problems of $$N_1$$-matrices and $$BN_1$$-matrices	6
A two-dimensional randomized extended Gauss-Seidel algorithm for solving least squares problems	6
An improved preconditioned inexact Uzawa method for elliptic optimal control problems	6
TT-LSQR for tensor least squares problems and application to data mining	6
Non-negative Einstein tensor factorization for unmixing hyperspectral images	6
Optimal size of the block in block GMRES on GPUs: computational model and experiments	6
On computing the zeros of a class of Sobolev orthogonal polynomials	6
Fast and accurate solvers for weakly singular integral equations	6
Adaptive time step selection for spectral deferred correction	6
Global convergence of a curvilinear search for non-convex optimization	6
Estimating error norms in CG-like algorithms for least-squares and least-norm problems	6
A novel numerical scheme for time-fractional Black-Scholes PDE governing European options in mathematical finance	5
Novel numerical methods based on graded, adaptive and uniform meshes for a time-fractional advection-diffusion equation subjected to weakly singular solution	5
A fast algorithm for time-fractional diffusion equation with space-time-dependent variable order	5
Modified projection method and strong convergence theorem for solving variational inequality problems with non-Lipschitz operators	5
A fast second-order scheme for nonlinear Riesz space-fractional diffusion equations	5
An inexact proximal majorization-minimization algorithm for remote sensing image stripe noise removal	5
Artificial compressibility SAV ensemble algorithms for the incompressible Navier-Stokes equations	5
Finite element approximation of optimal control problem with integral fractional Laplacian and state constraint	5
A projection algorithm for pseudomonotone vector fields with convex constraints on Hadamard manifolds	5
Operator-splitting finite element method for solving the radiative transfer equation	5
Refined and refined harmonic Jacobi–Davidson methods for computing several GSVD components of a large regular matrix pair	5
A hybrid-inertial accelerated spectral CG projection method with restart mechanism and its application to compressed sensing	5
Convergence properties of Jacobi gradient-based iteration algorithm for the complex conjugate and transpose Sylvester matrix equations	5
A μ-mode BLAS approach for multidimensional tensor-structured problems	5
Optimality and duality results for fractional programming problems under E-univexity	5
An adaptive nonmonotone line search technique for nonsmooth optimization	5
A highly efficient class of optimal fourth-order methods for solving nonlinear systems	5
Strong convergence and extinction of positivity preserving explicit scheme for the stochastic SIS epidemic model	5
Deviation maximization for rank-revealing QR factorizations	5
A high-order numerical scheme and its analysis for Caputo temporal-fractional Black-Scholes model: European double barrier knock-out option	5
On the computation of the cumulative distribution function of the normal inverse Gaussian distribution	5
An effective computational approach based on new multi-step collocation method for solving integral-algebraic equations	5
Equivalence and convergence analysis of fixed point iterative schemes using higher order averaged mappings	5
Fractal interpolation on the real projective plane	5
Accelerated iterative algorithms for the Cauchy problem in steady-state anisotropic heat conduction	5
Some combined techniques of spectral conjugate gradient methods with applications to robotic and image restoration models	5
RMPIA: a new algorithm for computing the Lagrange matrix interpolation polynomials	5
Hermite interpolation theorems for band-limited functions of the linear canonical transforms with equidistant samples	5
The global convergence of the BFGS method with a modified WWP line search for nonconvex functions	5
Reducing the truncation error in Taylor model multiplication	5
An efficient fractional step numerical algorithm for time-delayed singularly perturbed 2D convection-diffusion–reaction problem with two small parameters	5
C-FISTA type projection algorithm for quasi-variational inequalities	5
New structure-preserving algorithms of Gauss-Seidel and successive over-relaxation iteration methods for quaternion linear systems	5
Mixed noise removal via generalized gaussian scale mixture modeling and plug-and-play deep prior	5
A weak Galerkin finite element method for singularly perturbed problems with two small parameters on Bakhvalov-type meshes	5
Inertial accelerated primal-dual methods for linear equality constrained convex optimization problems	5
Two-level methods for solving higher order finite element discretizations of nonsymmetric and indefinite elliptic problem	5
Acceleration of sequences with transformations involving hypergeometric functions	5
A class of modified accelerated proximal gradient methods for nonsmooth and nonconvex minimization problems	5
Lagrange interpolation polynomials for solving nonlinear stochastic integral equations	5
A note on the Grcar matrix	5
The quaternion relaxed greedy randomized Kaczmarz method with adaptive parameters for solving quaternion matrix equation	5
Divergence of the Euler-Maruyama method for neutral stochastic differential equations with unbounded delay and Markovian switching	5
On the non-global linear stability and spurious fixed points of MPRK schemes with negative RK parameters	5
A fast stable accurate artificial boundary condition for the linearized Green-Naghdi system	5
Quantifying mixing in arbitrary fluid domains: a Padé approximation approach	5
Fast and stable rational approximation of generalized 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
A unified convergence analysis of random sketch methods for rank deficient linear systems	5
Approximation by polynomials in Sobolev spaces associated with classical moment functionals	4
Smooth connectivity in real algebraic varieties	4
Inertial self-adaptive algorithms for solving non-smooth convex optimization problems	4
High-order $$L^{2}$$-bound-preserving Fourier pseudo-spectral schemes for the Allen-Cahn equation	4
A new algorithm for solving a class of matrix optimization problem arising in unsupervised feature selection	4
Boundary reconstruction in two-dimensional steady-state anisotropic heat conduction	4
Correction to: fast and accurate numerical algorithm for solving stochastic itô-volterra integral equations	4
Compact finite difference schemes and error estimation for third-order Emden-Fowler equations	4
Approximate linearization of fixed-point iterations	4
Discrete mollification in Bernstein basis and space marching scheme for numerical solution of an inverse two-phase one-dimensional Stefan problem	4
Explicit representations of the norms of the Laguerre-Sobolev and Jacobi-Sobolev polynomials	4
Adaptive multiplication of $$\mathcal {H}^2$$-matrices with block-relative error control	4
Error analysis and accuracy improvement of the fast multipole method for the linearized Poisson-Boltzmann equation	4
Numerical solution of the boundary value problems for the biharmonic equations via quasiseparable representations	4
A second-order BDF convex splitting numerical scheme for the Ericksen-Leslie equation	4
Modified Newton-PBS method for solving a class of complex symmetric nonlinear systems	4
Globally convergent diagonal Polak–Ribière–Polyak like algorithm for nonlinear equations	4
HODLR3D: hierarchical matrices for N-body problems in three dimensions	4