Numerical Algorithms

Article	Citations
ENO-based high-order data-bounded and constrained positivity-preserving interpolation	69
Krylov iterative methods for linear least squares problems with linear equality constraints	45
Local and parallel finite element methods based on two-grid discretizations for the unsteady mixed Stokes-Darcy model with the Beavers-Joseph interface condition	38
Two novel numerical methods for gradient flows: generalizations of the Invariant Energy Quadratization method	29
Convergence properties of a new projection algorithm for pseudomonotone vector fields on hadamard manifolds	29
Optimal polynomial approximation to rational matrix functions using the Arnoldi algorithm	28
A multipoint flux mixed finite element method with mass-conservative characteristic finite element method for incompressible miscible displacement problem	27
A unified convergence analysis of the derivative-free projection-based method for constrained nonlinear monotone equations	27
New nonsingular H-matrix subclass with parameter-free infinity norm bounds and linear complementarity error estimates	26
Modified globally convergent Polak-Ribière-Polyak conjugate gradient methods with self-correcting property for large-scale unconstrained optimization	26
Correction to: Fitted schemes for Caputo-Hadamard fractional differential equations	24
The application of Goeken–Johnson’s Runge–Kutta methods in unconstrained convex optimization	24
A three-phase method for systematically and simultaneously computing multiple optimal solutions	23
A reduced SQP-type algorithm for nonlinear semidefinite programming with LMI constraints	23
TRIPs-Py: Techniques for regularization of inverse problems in python	22
Modulus-based synchronous multisplitting iteration methods for large sparse vertical linear complementarity problems	20
Positive quadrature formulas on an arc of the unit circle	20
A nondeterministic branch-and-bound algorithm for maximizing the sum of a generalized Rayleigh quotient and a quadratic form on the unit sphere	20
Numerical analysis of a linearly backward Euler method with truncated Wiener process for a stochastic SIS model	19
On the construction of iterative methods in (p,q)-calculus	19
Uniformly accurate nested Picard iterative integrators for the Klein-Gordon-Schrödinger equation in the nonrelativistic regime	19
The backward rounding error analysis of the quaternion Givens QR decomposition	18
On the dynamics of Steffensen’s family of root-finding methods for entire function	18
The linear barycentric rational backward differentiation formulae for stiff ODEs on nonuniform grids	18
Szegő quadrature formulas associated with the weight function $$1+\cos (m\theta )$$ with application to the approximation of certain Christoffel transformations on the interval	17

Implementation of divided differences to shape preservation	17
Multivariate polynomial interpolation based on Radon projections	17
Interlacing and bounds of zeros of quasi-orthogonal little q-Jacobi polynomials	17
Numerical solution to the exterior Bernoulli problem using the Dirichlet-Robin energy gap cost functional approach in two and three dimensions	17
Reducing swamp behavior for the canonical polyadic decomposition problem by rank-1 freezing	17
Correction to: “Patch area and uniform sampling on the surface of any ellipsoid”	16
On the accurate computation of the Newton form of the Lagrange interpolant	16
Modulus-based block triangular splitting iteration method for solving the generalized absolute value equations	16
Regularized Barzilai-Borwein Method	16
A class of new three-term descent conjugate gradient algorithms for large-scale unconstrained optimization and applications to image restoration problems	16
A novel banded preconditioner for coupled tempered fractional diffusion equation generated from the regime-switching CGMY model	16
Shift-splitting fixed point iteration method for solving generalized absolute value equations	16
Extrapolation quadrature from equispaced samples of functions with jumps	16
A spatial branch and bound algorithm for solving the sum of linear ratios optimization problem	16
Interpolated Galerkin finite elements on triangular meshes for the biharmonic equation	15
Orthogonal Cauchy-like matrices	15
Average-based iterative methods for solving nonlinear integral equations and systems of ordinary equations	15
Fourier transforms of orthogonal polynomials on the cone	15
High accuracy two-level compact implicit method in exponential form for 2D fourth order quasi-linear parabolic equations	15
Randomized flexible GMRES with deflated restarting	15
On the maximal order of convergence of Green’s function method for solving two-point boundary value problems with deviating argument	14
Improvements to steepest descent method for multi-objective optimization	14
Banded preconditioning with shift compensation for solving discrete Riesz space-fractional diffusion equations	14
An adaptive branch-and-bound algorithm for minimax linear fractional programming	14
Convergence analysis of Tikhonov regularized dynamical systems and inertial algorithms for convex optimization problems	14
Maximal residual coordinate descent method with k-means clustering for solving large linear least-squares problems	14
Preconditioned generalized minimal residual method for quaternion linear systems with structured coefficient matrices and its applications	13
On a class of infinite M-matrices with an extended quasi-Toeplitz structure	13
Solving non-differentiable Hammerstein integral equations via first-order divided differences	13
A mixed precision LOBPCG algorithm	13
High modes smoothing of time schemes for nonlinear parabolic PDEs	13
Decompose-then-optimize: a new approach to design domain decomposition methods for optimal control problems	13
A multidimensional Hermite-Gauss sampling formula for analytic functions of several variables	12
Complex moment-based methods for differential eigenvalue problems	12
A simple yet efficient two-step fifth-order weighted-Newton method for nonlinear models	12
Local and parallel stabilized finite element methods based on two-grid discretizations for the Stokes equations	11
General christoffel perturbations for multiple orthogonal polynomials of the mixed type on the step-line	11
Comments on “Fractal functions associated with Reich contractions: an approximation of chaotic attractors”	11
Maximum bound principle for matrix-valued Allen-Cahn equation and integrating factor Runge-Kutta method	11
Iteration methods for the classical split quaternion tensor equation $$\mathcal {E}*_N\mathcal {X}*_N\mathcal {F}=\mathcal {D}$$	11
First order strong approximation of Ait–Sahalia-type interest rate model with Poisson jumps	11
A fast second-order predictor-corrector method for a nonlinear time-fractional Benjamin-Bona-Mahony-Burgers equation	11
Greedy reconstruction algorithms for function approximation	11
A numerical method based on Legendre wavelet and quasilinearization technique for fractional Lane-Emden type equations	11
Adaptive cross approximation for Tikhonov regularization in general form	11
Superconvergence and postprocessing of discontinuous Galerkin solutions for weakly singular Volterra integral equations	10
Inertial subgradient splitting projection methods for solving equilibrium problems and applications	10
Higher-order recurrence relations, Sobolev-type inner products and matrix factorizations	10
Fitted schemes for Caputo-Hadamard fractional differential equations	10
Optimal Control problems of NS-$$\alpha $$ and NS-$$\omega $$ turbulence models: analysis and numerical tests	10

Averaged cubature schemes on the real positive semiaxis	10
On unconditional stability of a penalty-based ensemble method	10
A family of gradient methods using Householder transformation with application to hypergraph partitioning	10
Fast computation of best approximation polynomials for the reciprocal function	10
Communication in multiplex transportation networks	10
Incomplete double-cone factorizations of centrosymmetric matrices arising in spectral methods	10
Optimized Schwarz domain decomposition algorithms for the closest point method on closed manifolds	10
Greedy adaptive local recovery of functions in Sobolev spaces	10
Douglas-Rachford iterations for the HSS splitting	10
Integrable semi-discretizations and self-adaptive moving mesh method for a generalized sine-Gordon equation	9
Optimal error estimate of the penalty method for the 2D/3D time-dependent MHD equations	9
Vem++, a C++ library to handle and play with the virtual element method	9
On the extension of a class of Hermite multivariate interpolation problems	9
Polynomial estimates for the method of cyclic projections in Hilbert spaces	9
Constructing Sobolev orthonormal rational functions via an updating procedure	9
A modified spectral three-term hybrid derivative-free projection method using convex combination acceleration to solve nonlinear complementarity problems	9
A three-step modulus-based iterative method for solving nonlinear complementarity problems	9
A non-linear conjugate gradient in dual space for $$L_p$$-norm regularized non-linear least squares with application in data assimilation	9
Fractional-order Chelyshkov wavelet method for solving variable-order fractional differential equations and an application in variable-order fractional relaxation system	9
Solving semi-discrete optimal transport problems: star shapedeness and Newton’s method	9
Global convergence of a spectral conjugate gradient method for unconstrained optimization	9
Logarithmic function minimization to compressed sensing with application to magnetic resonance imaging	9
Interpolation preservation of AMF-W methods for linear diffusion problems	9
The truncated Euler-Maruyama method for highly nonlinear stochastic differential equations with multiple time delays	9
A two-grid combined mixed finite element and discontinuous Galerkin method for a compressible miscible displacement problem	9
Preconditioned inexact fixed point iteration method for solving tensor absolute value equation	9
Analysis of the basins of attraction generated by a pseudo Newton-Raphson method iterating over complex order derivatives	9
Applications of quasideterminants to non-commutative multistep $$\varepsilon $$-algorithm	9
A difference-of-convex approach for log-determinant semidefinite programming with chordal sparsity	9
Proximal variable smoothing method for three-composite nonconvex nonsmooth minimization with a linear operator	9
A new approach of shifted Jacobi spectral Galerkin methods (SJSGM) for weakly singular Fredholm integral equation with non-smooth solution	9
Smaller stencil preconditioners for linear systems in RBF-FD discretizations	8
Analysis of Julia sets using viscosity approximation-based iteration processes	8
Exact subdomain and embedded interface polynomial integration in finite elements with planar cuts	8
Computing Gaussian quadrature rules with high relative accuracy	8
Exploring rational approximations of fractional power operators for preconditioning	8
EDECT algorithm: The hybridization of the filled function and DIRECT methods for global optimization	8
Accuracy and stability of the column pivoting quaternion Householder QR factorization	8
Extended explicit Pseudo two-step Runge-Kutta-Nyström methods for general second-order oscillatory systems	8
Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the third and fourth kinds	8
Non-linear WENO B-spline based approximation method	8
Accurate inverses and determinants of doubly strictly diagonally dominant Z-matrices	8
A robust variant of cubic smoothing spline approximation	8
Correction to: High-order linearly implicit exponential integrators conserving quadratic invariants with application to scalar auxiliary variable approach	8
Fractional Legendre wavelet approach resolving multi-scale optimal control problems involving Caputo-Fabrizio derivative	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
Inertial Bregman proximal gradient under partial smoothness	8
Alternated inertial algorithms for split feasibility problems	8
Deep learning, transformers and graph neural networks: a linear algebra perspective	8
Stochastic parareal algorithm for stochastic differential equations	7
Locally conservative discontinuous bubble scheme for Darcy flow and its application to Hele-Shaw equation based on structured grids	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
Adaptive time step selection for spectral deferred correction	7
The method of randomized Bregman projections for stochastic feasibility problems	7
TT-LSQR for tensor least squares problems and application to data mining	7
Sliding modes of high codimension in piecewise-smooth dynamical systems	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
An orthogonal randomized Bregman projection method for linearly constrained optimization problems	7
Legendre polynomial based approximation of the Hessian for quasi-Newton optimization	7
Stochastic incremental mirror descent algorithms with Nesterov smoothing	7
H-representation method for the least squares symmetric solutions of the reduced biquaternion matrix equation and its application in color image restoration	7
The behavior of the Gauss-Radau upper bound of the error norm in CG	7
Optimal polynomial smoothers for parallel AMG	7
Source-to-sink communicability: a new centrality measure for directed acyclic networks	7
Unconditionally positivity-preserving approximations of the Aït-Sahalia type model: Explicit Milstein-type schemes	7
Fully numerical Laplace transform methods	7
Nonmonotone Quasi–Newton-based conjugate gradient methods with application to signal processing	7
Revisiting the (block) Jacobi subspace rotation method for the symmetric eigenvalue problem	7
Generalized discrete Lotka-Volterra equation, orthogonal polynomials and generalized epsilon algorithm	7
Fast superconvergent solvers for weakly singular Hammerstein equations	7
An MP-DWR method for h-adaptive finite element methods	7
A new family of fourth-order energy-preserving integrators	7
Unconditionally energy stable IEQ-FEMs for the Cahn-Hilliard equation and Allen-Cahn equation	7
A stable second-order difference scheme for the generalized time-fractional non-Fickian delay reaction-diffusion equations	7
A Numerical Approach for the System of Nonlinear Variable-order Fractional Volterra Integral Equations	7
New proximal bundle algorithm based on the gradient sampling method for nonsmooth nonconvex optimization with exact and inexact information	7
Non-blind constraint image deblurring problem with mean curvature functional	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
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
Reconstruction of missing boundary data for nonlinear parabolic systems using a control-type approach	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
A projection algorithm for pseudomonotone vector fields with convex constraints on Hadamard manifolds	6
Global convergence of a curvilinear search for non-convex optimization	6
Interpolated Galerkin finite elements on rectangular and cuboid meshes for the Poisson equation	6
A nonsmooth Newton method for solving the generalized complementarity problem	6
Fast and low-memory compressive sensing algorithms for low tucker-rank tensor approximation from streamed measurements	6
Optimal size of the block in block GMRES on GPUs: computational model and experiments	6
Fast and accurate solvers for weakly singular integral equations	6
A two-dimensional randomized extended Gauss-Seidel algorithm for solving least squares problems	6
Estimating error norms in CG-like algorithms for least-squares and least-norm problems	6
Boundary corrections on multi-dimensional PDEs	6
A two-step inertial Hager-Zhang derivative-free projection method for solving nonlinear equations with applications	6
A fourth-order collocation scheme for generalized Black-Scholes model in financial decision-making	6
The generalized modular string averaging procedure and its applications to iterative methods for solving various nonlinear operator theory problems	6
An adaptive nonmonotone line search technique for nonsmooth optimization	6
Refined and refined harmonic Jacobi–Davidson methods for computing several GSVD components of a large regular matrix pair	6
Results on split common fixed point problems: applications to signal and image restoration	6
Tensor Interpolation	6
A new optimal root-finding iterative algorithm: local and semilocal analysis with polynomiography	6
Another Hager-Zhang-type method via singular-value study for constrained monotone equations with application	6
Error bounds for the linear complementarity problems of $$N_1$$-matrices and $$BN_1$$-matrices	6
Inexact quasi-Newton methods under a relaxed metric regularity assumption	6
On computing the zeros of a class of Sobolev orthogonal polynomials	6
A numerical algorithm for asymptotically approximating the solution to periodic tridiagonal Toeplitz linear systems	6
Stieltjes interlacing of zeros of little q-Jacobi and q-Laguerre polynomials from different sequences	6
A predictor-corrector finite element method for parabolic problems on polygonal domains	6
Fractal interpolation on the real projective plane	6
Max-convolution through numerics and tropical geometry	6
A weak Galerkin finite element method for singularly perturbed problems with two small parameters on Bakhvalov-type meshes	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
An efficient numerical algorithm based on Haar wavelets for multi-dimensional nonlinear elliptic PDEs	6
An improved preconditioned inexact Uzawa method for elliptic optimal control problems	6
A projection DFP quasi-Newton algorithm and its applications in Muskingum model and machine learning	6
Limited memory gradient methods for unconstrained optimization	6
Approximation of 2D function with a jump discontinuity - the high noise case	5
On the computation of the cumulative distribution function of the normal inverse Gaussian distribution	5
Riemannian Barzilai–Borwein method for the hermitian quaternion eigenvalue problem	5
Accelerated iterative algorithms for the Cauchy problem in steady-state anisotropic heat conduction	5
An inexact proximal majorization-minimization algorithm for remote sensing image stripe noise removal	5
A class of modified accelerated proximal gradient methods for nonsmooth and nonconvex minimization problems	5
A conformable fractional iterative fixed-point method for solving one-dimensional nonlinear equations	5
On the non-global linear stability and spurious fixed points of MPRK schemes with negative RK parameters	5
Four double inertial algorithms for variational inequalities with fixed point constraints: theory and signal processing applications	5
Two-level methods for solving higher order finite element discretizations of nonsymmetric and indefinite elliptic problem	5
A fast second-order scheme for nonlinear Riesz space-fractional diffusion equations	5
A high-order numerical scheme and its analysis for Caputo temporal-fractional Black-Scholes model: European double barrier knock-out option	5
New structure-preserving algorithms of Gauss-Seidel and successive over-relaxation iteration methods for quaternion linear systems	5
Modified projection method and strong convergence theorem for solving variational inequality problems with non-Lipschitz operators	5
$$O(1/k^2)$$ convergence rates of (dual-primal) balanced augmented Lagrangian methods for linearly constrained convex programming	5
Optimal adaptive numerical methods for ODEs via stable robust global error control	5
Reducing the truncation error in Taylor model multiplication	5
A nonlinear conjugate gradient method for solving quaternion matrix equation and its application in color image encryption and decryption	5
Strong convergence and extinction of positivity preserving explicit scheme for the stochastic SIS epidemic model	5
An effective computational approach based on new multi-step collocation method for solving integral-algebraic equations	5
A fast algorithm for time-fractional diffusion equation with space-time-dependent variable order	5
Convergence properties of Jacobi gradient-based iteration algorithm for the complex conjugate and transpose Sylvester matrix equations	5
A hybrid-inertial accelerated spectral CG projection method with restart mechanism and its application to compressed sensing	5
Hermite interpolation theorems for band-limited functions of the linear canonical transforms with equidistant samples	5
A novel numerical scheme for time-fractional Black-Scholes PDE governing European options in mathematical finance	5
The quaternion relaxed greedy randomized Kaczmarz method with adaptive parameters for solving quaternion matrix equation	5
Operator-splitting finite element method for solving the radiative transfer equation	5
Mixed noise removal via generalized gaussian scale mixture modeling and plug-and-play deep prior	5
A unified convergence analysis of random sketch methods for rank deficient linear systems	5
Quantifying mixing in arbitrary fluid domains: a Padé approximation approach	5
On the convergence of two-step modified Newton method for nonsymmetric algebraic Riccati equations from transport theory	5
C-FISTA type projection algorithm for quasi-variational inequalities	5
Some combined techniques of spectral conjugate gradient methods with applications to robotic and image restoration models	5
Artificial compressibility SAV ensemble algorithms for the incompressible Navier-Stokes equations	5
A note on the Grcar matrix	5
Divergence of the Euler-Maruyama method for neutral stochastic differential equations with unbounded delay and Markovian switching	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
HODLR3D: hierarchical matrices for N-body problems in three dimensions	4
Fast Euler–Maruyama method for weakly singular stochastic Volterra integral equations with variable exponent	4
Relaxed Tseng splitting method with double inertial steps for solving monotone inclusions and fixed point problems	4
Globally convergent diagonal Polak–Ribière–Polyak like algorithm for nonlinear equations	4
A weak Galerkin pseudostress-based mixed finite element method on polygonal meshes: application to the Brinkman problem appearing in porous media	4
Numerical solution of the boundary value problems for the biharmonic equations via quasiseparable representations	4
Adaptive multiplication of $$\mathcal {H}^2$$-matrices with block-relative error control	4
Nitsche’s method under a semi-regular mesh condition	4
Enhancing image restoration using a discrete variational model with triangular mesh-based TV	4
Variable parameter Uzawa method for solving the indefinite least squares problem	4
Modified Newton-PBS method for solving a class of complex symmetric nonlinear systems	4
Inertial self-adaptive algorithms for solving non-smooth convex optimization problems	4
Improved Gegenbauer spectral tau algorithms for distributed-order time-fractional telegraph models in multi-dimensions	4
An efficient three-term conjugate gradient method with adaptive regularization and its application in image restoration	4
On the convergence of Galerkin methods for auto-convolution Volterra integro-differential equations	4
A second-order BDF convex splitting numerical scheme for the Ericksen-Leslie equation	4
Explicit representations of the norms of the Laguerre-Sobolev and Jacobi-Sobolev polynomials	4
Boundary reconstruction in two-dimensional steady-state anisotropic heat conduction	4