Numerical Algorithms

Article	Citations
ENO-based high-order data-bounded and constrained positivity-preserving interpolation	66
Krylov iterative methods for linear least squares problems with linear equality constraints	44
Several accelerated subspace minimization conjugate gradient methods based on regularization model and convergence rate analysis for nonconvex problems	35
Local and parallel finite element methods based on two-grid discretizations for the unsteady mixed Stokes-Darcy model with the Beavers-Joseph interface condition	31
Two novel numerical methods for gradient flows: generalizations of the Invariant Energy Quadratization method	28
Convergence, weak w2 stability, and data dependence results for the F iterative scheme in hyperbolic spaces	26
Convergence properties of a new projection algorithm for pseudomonotone vector fields on hadamard manifolds	26
A multipoint flux mixed finite element method with mass-conservative characteristic finite element method for incompressible miscible displacement problem	26
Optimal polynomial approximation to rational matrix functions using the Arnoldi algorithm	26
Modified globally convergent Polak-Ribière-Polyak conjugate gradient methods with self-correcting property for large-scale unconstrained optimization	25
A unified convergence analysis of the derivative-free projection-based method for constrained nonlinear monotone equations	25
New nonsingular H-matrix subclass with parameter-free infinity norm bounds and linear complementarity error estimates	24
The application of Goeken–Johnson’s Runge–Kutta methods in unconstrained convex optimization	23
On the construction of iterative methods in (p,q)-calculus	23
Correction to: Fitted schemes for Caputo-Hadamard fractional differential equations	22
A three-phase method for systematically and simultaneously computing multiple optimal solutions	22
TRIPs-Py: Techniques for regularization of inverse problems in python	20
A reduced SQP-type algorithm for nonlinear semidefinite programming with LMI constraints	20
Numerical analysis of a linearly backward Euler method with truncated Wiener process for a stochastic SIS model	18
Reducing swamp behavior for the canonical polyadic decomposition problem by rank-1 freezing	18
Modulus-based synchronous multisplitting iteration methods for large sparse vertical linear complementarity problems	18
A nondeterministic branch-and-bound algorithm for maximizing the sum of a generalized Rayleigh quotient and a quadratic form on the unit sphere	18
Positive quadrature formulas on an arc of the unit circle	18
Fast solution method and simulation for the 2D time-space fractional Black-Scholes equation governing European two-asset option pricing	18
The linear barycentric rational backward differentiation formulae for stiff ODEs on nonuniform grids	17

Balanced-norm error estimate of the local discontinuous Galerkin method on layer-adapted meshes for reaction-diffusion problems	17
Interlacing and bounds of zeros of quasi-orthogonal little q-Jacobi polynomials	17
Implementation of divided differences to shape preservation	17
Uniformly accurate nested Picard iterative integrators for the Klein-Gordon-Schrödinger equation in the nonrelativistic regime	17
On the dynamics of Steffensen’s family of root-finding methods for entire function	17
The backward rounding error analysis of the quaternion Givens QR decomposition	17
Numerical solution to the exterior Bernoulli problem using the Dirichlet-Robin energy gap cost functional approach in two and three dimensions	16
Multivariate polynomial interpolation based on Radon projections	16
A mixed precision LOBPCG algorithm	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	16
Banded preconditioning with shift compensation for solving discrete Riesz space-fractional diffusion equations	16
Modulus-based block triangular splitting iteration method for solving the generalized absolute value equations	16
Improvements to steepest descent method for multi-objective optimization	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	15
A spatial branch and bound algorithm for solving the sum of linear ratios optimization problem	15
On the accurate computation of the Newton form of the Lagrange interpolant	15
Correction to: “Patch area and uniform sampling on the surface of any ellipsoid”	15
Regularized Barzilai-Borwein Method	15
Extrapolation quadrature from equispaced samples of functions with jumps	15
Shift-splitting fixed point iteration method for solving generalized absolute value equations	15
Orthogonal Cauchy-like matrices	14
Total positivity and accurate computations with Gram matrices of Bernstein bases	14
High accuracy two-level compact implicit method in exponential form for 2D fourth order quasi-linear parabolic equations	14
Interpolated Galerkin finite elements on triangular meshes for the biharmonic equation	14
Average-based iterative methods for solving nonlinear integral equations and systems of ordinary equations	13
High modes smoothing of time schemes for nonlinear parabolic PDEs	13
Preconditioned generalized minimal residual method for quaternion linear systems with structured coefficient matrices and its applications	13
Solving non-differentiable Hammerstein integral equations via first-order divided differences	13
On the maximal order of convergence of Green’s function method for solving two-point boundary value problems with deviating argument	13
Decompose-then-optimize: a new approach to design domain decomposition methods for optimal control problems	13
Fourier transforms of orthogonal polynomials on the cone	13
On a class of infinite M-matrices with an extended quasi-Toeplitz structure	13
A multidimensional Hermite-Gauss sampling formula for analytic functions of several variables	12
An adaptive branch-and-bound algorithm for minimax linear fractional programming	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
Maximal residual coordinate descent method with k-means clustering for solving large linear least-squares problems	12
Randomized flexible GMRES with deflated restarting	12
Global convergence of a spectral conjugate gradient method for unconstrained optimization	11
On unconditional stability of a penalty-based ensemble method	11
Applications of quasideterminants to non-commutative multistep $$\varepsilon $$-algorithm	11
Iteration methods for the classical split quaternion tensor equation $$\mathcal {E}*_N\mathcal {X}*_N\mathcal {F}=\mathcal {D}$$	11
Averaged cubature schemes on the real positive semiaxis	11
Incomplete double-cone factorizations of centrosymmetric matrices arising in spectral methods	11
Superconvergence and postprocessing of discontinuous Galerkin solutions for weakly singular Volterra integral equations	10
General christoffel perturbations for multiple orthogonal polynomials of the mixed type on the step-line	10
Logarithmic function minimization to compressed sensing with application to magnetic resonance imaging	10
Communication in multiplex transportation networks	10
Maximum bound principle for matrix-valued Allen-Cahn equation and integrating factor Runge-Kutta method	10

First order strong approximation of Ait–Sahalia-type interest rate model with Poisson jumps	10
Optimal Control problems of NS-$$\alpha $$ and NS-$$\omega $$ turbulence models: analysis and numerical tests	10
A family of gradient methods using Householder transformation with application to hypergraph partitioning	10
A numerical method based on Legendre wavelet and quasilinearization technique for fractional Lane-Emden type equations	10
Greedy reconstruction algorithms for function approximation	10
Optimized Schwarz domain decomposition algorithms for the closest point method on closed manifolds	10
Analysis of the basins of attraction generated by a pseudo Newton-Raphson method iterating over complex order derivatives	10
Adaptive cross approximation for Tikhonov regularization in general form	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
Douglas-Rachford iterations for the HSS splitting	9
Fitted schemes for Caputo-Hadamard fractional differential equations	9
Proximal variable smoothing method for three-composite nonconvex nonsmooth minimization with a linear operator	9
Solving semi-discrete optimal transport problems: star shapedeness and Newton’s method	9
Interpolation preservation of AMF-W methods for linear diffusion problems	9
A two-grid combined mixed finite element and discontinuous Galerkin method for a compressible miscible displacement problem	9
A fast second-order predictor-corrector method for a nonlinear time-fractional Benjamin-Bona-Mahony-Burgers equation	9
A difference-of-convex approach for log-determinant semidefinite programming with chordal sparsity	9
Vem++, a C++ library to handle and play with the virtual element method	9
Comments on “Fractal functions associated with Reich contractions: an approximation of chaotic attractors”	9
Optimal error estimate of the penalty method for the 2D/3D time-dependent MHD equations	9
Polynomial estimates for the method of cyclic projections in Hilbert spaces	9
Local and parallel stabilized finite element methods based on two-grid discretizations for the Stokes equations	9
Greedy adaptive local recovery of functions in Sobolev spaces	9
Fast computation of best approximation polynomials for the reciprocal function	9
Preconditioned inexact fixed point iteration method for solving tensor absolute value equation	9
Fractional-order Chelyshkov wavelet method for solving variable-order fractional differential equations and an application in variable-order fractional relaxation system	9
Integrable semi-discretizations and self-adaptive moving mesh method for a generalized sine-Gordon equation	9
A non-linear conjugate gradient in dual space for $$L_p$$-norm regularized non-linear least squares with application in data assimilation	8
Constructing Sobolev orthonormal rational functions via an updating procedure	8
Exploring rational approximations of fractional power operators for preconditioning	8
A three-step modulus-based iterative method for solving nonlinear complementarity problems	8
Smaller stencil preconditioners for linear systems in RBF-FD discretizations	8
Legendre polynomial based approximation of the Hessian for quasi-Newton optimization	8
Inertial Bregman proximal gradient under partial smoothness	8
Correction to: High-order linearly implicit exponential integrators conserving quadratic invariants with application to scalar auxiliary variable approach	8
A modified spectral three-term hybrid derivative-free projection method using convex combination acceleration to solve nonlinear complementarity problems	8
Deep learning, transformers and graph neural networks: a linear algebra perspective	8
Alternated inertial algorithms for split feasibility problems	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
Accurate inverses and determinants of doubly strictly diagonally dominant Z-matrices	8
EDECT algorithm: The hybridization of the filled function and DIRECT methods for global optimization	8
A robust variant of cubic smoothing spline approximation	8
Analysis of Julia sets using viscosity approximation-based iteration processes	8
Extended explicit Pseudo two-step Runge-Kutta-Nyström methods for general second-order oscillatory systems	8
The truncated Euler-Maruyama method for highly nonlinear stochastic differential equations with multiple time delays	8
Computing Gaussian quadrature rules with high relative accuracy	8
Non-linear WENO B-spline based approximation method	7
A new family of fourth-order energy-preserving integrators	7
A stable second-order difference scheme for the generalized time-fractional non-Fickian delay reaction-diffusion equations	7
A predictor-corrector finite element method for parabolic problems on polygonal domains	7
An incomplete tridiagonalization-based determinant evaluation for a generalized periodic tridiagonal matrix	7
An MP-DWR method for h-adaptive finite element methods	7
A variational regularization method for solving the non-characteristic Cauchy problem in multiple dimensions	7
Unconditionally positivity-preserving approximations of the Aït-Sahalia type model: Explicit Milstein-type schemes	7
The behavior of the Gauss-Radau upper bound of the error norm in CG	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
Stochastic incremental mirror descent algorithms with Nesterov smoothing	7
Analysis of a higher-order scheme for multi-term time-fractional integro-partial differential equations with multi-term weakly singular kernels	7
A new modified Mann-type method for solving the monotone inclusion problem and the fixed point problem in reflexive Banach spaces	7
Nonmonotone Quasi–Newton-based conjugate gradient methods with application to signal processing	7
Unconditionally energy stable IEQ-FEMs for the Cahn-Hilliard equation and Allen-Cahn equation	7
Revisiting the (block) Jacobi subspace rotation method for the symmetric eigenvalue problem	7
Runge–Kutta methods determined from extended phase space methods for Hamiltonian systems	7
A fault detection method based on partition of unity and kernel approximation	7
Stochastic parareal algorithm for stochastic differential equations	7
Fast superconvergent solvers for weakly singular Hammerstein equations	7
An orthogonal randomized Bregman projection method for linearly constrained optimization problems	7
Non-blind constraint image deblurring problem with mean curvature functional	7
Exact subdomain and embedded interface polynomial integration in finite elements with planar cuts	7
Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the third and fourth kinds	7
Piecewise numerical approach for solving piecewise fractional optimal control and variational problems	7
New proximal bundle algorithm based on the gradient sampling method for nonsmooth nonconvex optimization with exact and inexact information	7
Sliding modes of high codimension in piecewise-smooth dynamical systems	7
Source-to-sink communicability: a new centrality measure for directed acyclic networks	7
H-representation method for the least squares symmetric solutions of the reduced biquaternion matrix equation and its application in color image restoration	7
Locally conservative discontinuous bubble scheme for Darcy flow and its application to Hele-Shaw equation based on structured grids	7
Generalized discrete Lotka-Volterra equation, orthogonal polynomials and generalized epsilon algorithm	7
Fully numerical Laplace transform methods	7

Fractional Legendre wavelet approach resolving multi-scale optimal control problems involving Caputo-Fabrizio derivative	7
Comprehensive deep contrastive manifold regularized non-negative matrix factorization for multi-view clustering	7
Interpolated Galerkin finite elements on rectangular and cuboid meshes for the Poisson equation	6
Max-convolution through numerics and tropical geometry	6
Adaptive time step selection for spectral deferred correction	6
Explicit numerical methods for solving singular initial value problems for systems of second-order nonlinear ODEs	6
Limited memory gradient methods for unconstrained optimization	6
Optimal size of the block in block GMRES on GPUs: computational model and experiments	6
A Numerical Approach for the System of Nonlinear Variable-order Fractional Volterra Integral Equations	6
The generalized modular string averaging procedure and its applications to iterative methods for solving various nonlinear operator theory problems	6
Tensor Interpolation	6
A two-step inertial Hager-Zhang derivative-free projection method for solving nonlinear equations with applications	6
TT-LSQR for tensor least squares problems and application to data mining	6
A numerical algorithm for asymptotically approximating the solution to periodic tridiagonal Toeplitz linear systems	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
Global convergence of a curvilinear search for non-convex optimization	6
A projection DFP quasi-Newton algorithm and its applications in Muskingum model and machine learning	6
An efficient numerical algorithm based on Haar wavelets for multi-dimensional nonlinear elliptic PDEs	6
Boundary corrections on multi-dimensional PDEs	6
Inexact quasi-Newton methods under a relaxed metric regularity assumption	6
A nonsmooth Newton method for solving the generalized complementarity problem	6
Fading regularization MFS algorithm for the Cauchy problem associated with the two-dimensional Stokes equations	6
The method of randomized Bregman projections for stochastic feasibility problems	6
Fast and low-memory compressive sensing algorithms for low tucker-rank tensor approximation from streamed measurements	6
Non-negative Einstein tensor factorization for unmixing hyperspectral images	6
Reconstruction of missing boundary data for nonlinear parabolic systems using a control-type approach	6
On the convergence of two-step modified Newton method for nonsymmetric algebraic Riccati equations from transport theory	6
A hybrid gradient method for vector optimization problems	6
A new optimal root-finding iterative algorithm: local and semilocal analysis with polynomiography	6
On computing the zeros of a class of Sobolev orthogonal polynomials	6
Another Hager-Zhang-type method via singular-value study for constrained monotone equations with application	6
Stieltjes interlacing of zeros of little q-Jacobi and q-Laguerre polynomials from different sequences	6
A fourth-order collocation scheme for generalized Black-Scholes model in financial decision-making	6
Fast and accurate solvers for weakly singular integral equations	6
Estimating error norms in CG-like algorithms for least-squares and least-norm problems	6
Optimal polynomial smoothers for parallel AMG	6
Error bounds for the linear complementarity problems of $$N_1$$-matrices and $$BN_1$$-matrices	6
An adaptive nonmonotone line search technique for nonsmooth optimization	5
A unified convergence analysis of random sketch methods for rank deficient linear systems	5
Some combined techniques of spectral conjugate gradient methods with applications to robotic and image restoration models	5
An inexact proximal majorization-minimization algorithm for remote sensing image stripe noise removal	5
Strong convergence and extinction of positivity preserving explicit scheme for the stochastic SIS epidemic model	5
A conformable fractional iterative fixed-point method for solving one-dimensional nonlinear equations	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
On the computation of the cumulative distribution function of the normal inverse Gaussian distribution	5
Accelerated iterative algorithms for the Cauchy problem in steady-state anisotropic heat conduction	5
A nonlinear conjugate gradient method for solving quaternion matrix equation and its application in color image encryption and decryption	5
A highly efficient class of optimal fourth-order methods for solving nonlinear systems	5
Hermite interpolation theorems for band-limited functions of the linear canonical transforms with equidistant samples	5
Artificial compressibility SAV ensemble algorithms for the incompressible Navier-Stokes equations	5
Convergence properties of Jacobi gradient-based iteration algorithm for the complex conjugate and transpose Sylvester matrix equations	5
Acceleration of sequences with transformations involving hypergeometric functions	5
New structure-preserving algorithms of Gauss-Seidel and successive over-relaxation iteration methods for quaternion linear systems	5
C-FISTA type projection algorithm for quasi-variational inequalities	5
Two-level methods for solving higher order finite element discretizations of nonsymmetric and indefinite elliptic problem	5
A note on the Grcar matrix	5
Four double inertial algorithms for variational inequalities with fixed point constraints: theory and signal processing applications	5
Fractal interpolation on the real projective plane	5
Truncated multidimensional moment problem and Schur algorithm	5
Modified projection method and strong convergence theorem for solving variational inequality problems with non-Lipschitz operators	5
Riemannian Barzilai–Borwein method for the hermitian quaternion eigenvalue problem	5
Divergence of the Euler-Maruyama method for neutral stochastic differential equations with unbounded delay and Markovian switching	5
A closest point method library for PDEs on surfaces with parallel domain decomposition solvers and preconditioners	5
A weak Galerkin finite element method for singularly perturbed problems with two small parameters on Bakhvalov-type meshes	5
Approximation of 2D function with a jump discontinuity - the high noise case	5
An effective computational approach based on new multi-step collocation method for solving integral-algebraic equations	5
Quantifying mixing in arbitrary fluid domains: a Padé approximation approach	5
Refined and refined harmonic Jacobi–Davidson methods for computing several GSVD components of a large regular matrix pair	5
Mixed noise removal via generalized gaussian scale mixture modeling and plug-and-play deep prior	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
On the non-global linear stability and spurious fixed points of MPRK schemes with negative RK parameters	5
A projection algorithm for pseudomonotone vector fields with convex constraints on Hadamard manifolds	5
A novel numerical scheme for time-fractional Black-Scholes PDE governing European options in mathematical finance	5
Fast and stable rational approximation of generalized hypergeometric functions	5
Operator-splitting finite element method for solving the radiative transfer equation	5
A hybrid-inertial accelerated spectral CG projection method with restart mechanism and its application to compressed sensing	5
Two new self-adaptive algorithms for solving the split feasibility problem in Hilbert space	5
A fast algorithm for time-fractional diffusion equation with space-time-dependent variable order	5
$$O(1/k^2)$$ convergence rates of (dual-primal) balanced augmented Lagrangian methods for linearly constrained convex programming	5
A class of modified accelerated proximal gradient methods for nonsmooth and nonconvex minimization problems	5
Reducing the truncation error in Taylor model multiplication	5
Nitsche’s method under a semi-regular mesh condition	4
Relaxed Tseng splitting method with double inertial steps for solving monotone inclusions and fixed point problems	4
Modified Newton-PBS method for solving a class of complex symmetric nonlinear systems	4
Boundary reconstruction in two-dimensional steady-state anisotropic heat conduction	4
A stage-wise homotopy ADMM for solving nonconvex quadratic programming problem	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
Globally convergent diagonal Polak–Ribière–Polyak like algorithm for nonlinear equations	4
Numerical solution of the boundary value problems for the biharmonic equations via quasiseparable representations	4
Another HSS iteration method	4
Variable parameter Uzawa method for solving the indefinite least squares problem	4
HODLR3D: hierarchical matrices for N-body problems in three dimensions	4