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research-article
A generalized cyclic iterative method for solving variational inequalities over the solution set of a split common fixed point problem
Abstract

We introduce a new generalized cyclic iterative method for finding solutions of variational inequalities over the solution set of a split common fixed point problem with multiple output sets in a real Hilbert space.

research-article
Improved two-step Newton’s method for computing simple multiple zeros of polynomial systems
Abstract

Given a polynomial system f that is associated with an isolated singular zero ξ whose Jacobian matrix is of corank one, and an approximate zero x that is close to ξ, we propose an improved two-step Newton’s method for refining x to converge to ξ ...

research-article
A class of C2 quasi-interpolating splines free of Gibbs phenomenon
Abstract

In many applications, it is useful to use piecewise polynomials that satisfy certain regularity conditions at the joint points. Cubic spline functions emerge as good candidates having C2 regularity. On the other hand, if the data points present ...

research-article
Linear and nonlinear substructured Restricted Additive Schwarz iterations and preconditioning
Abstract

Iterative substructuring Domain Decomposition (DD) methods have been extensively studied, and they are usually associated with nonoverlapping decompositions. It is less known that classical overlapping DD methods can also be formulated in ...

research-article
On the rational approximation of Markov functions, with applications to the computation of Markov functions of Toeplitz matrices
Abstract

We investigate the problem of approximating the matrix function f(A) by r(A), with f a Markov function, r a rational interpolant of f, and A a symmetric Toeplitz matrix. In a first step, we obtain a new upper bound for the relative interpolation ...

research-article
Adaptive three-term PRP algorithms without gradient Lipschitz continuity condition for nonconvex functions
Abstract

At present, many conjugate gradient methods with global convergence have been proposed in unconstrained optimization, such as MPRP algorithm proposed by Zhang et al. (IMA J. Numer. Anal.26(4):629–640, 2006). Unfortunately, almost all of these ...

research-article
A new family of hybrid three-term conjugate gradient methods with applications in image restoration
Abstract

In this paper, based on the hybrid conjugate gradient method and the convex combination technique, a new family of hybrid three-term conjugate gradient methods are proposed for solving unconstrained optimization. The conjugate parameter in the ...

research-article
An adaptive mesh refinement method for indirectly solving optimal control problems
Abstract

The indirect solution of optimal control problems (OCPs) with inequality constraints and parameters is obtained by solving the two-point boundary value problem (BVP) involving index-1 differential-algebraic equations (DAEs) associated with its ...

research-article
Generalized second derivative linear multistep methods for ordinary differential equations
Abstract

This paper is devoted to investigate the modified extended second derivative backward differentiation formulae from second derivative general linear methods point of view. This makes it possible to open some maneuver rooms in developing the ...

research-article
In reference to a self-referential approach towards smooth multivariate approximation
Abstract

Approximation of a multivariate function is an important theme in the field of numerical analysis and its applications, which continues to receive a constant attention. In this paper, we provide a parameterized family of self-referential (fractal) ...

research-article
A variant of PMHSS iteration method for a class of complex symmetric indefinite linear systems
Abstract

We propose a variant of PMHSS iteration method for solving and preconditioning a class of complex symmetric indefinite linear systems. The unconditional convergence theory of this iteration method is proved, and the choice of quasi-optimal ...

research-article
Public Access
Numerical approximation of the spectrum of self-adjoint operators in operator preconditioning
Abstract

We consider operator preconditioning B1A, which is employed in the numerical solution of boundary value problems. Here, the self-adjoint operators A,B:H01(Ω)H1(Ω) are the standard integral/functional representations of the partial differential ...

research-article
A second-order dynamical system for equilibrium problems
Abstract

We consider a second-order dynamical system for solving equilibrium problems in Hilbert spaces. Under mild conditions, we prove existence and uniqueness of strong global solution of the proposed dynamical system. We establish the exponential ...

research-article
The global convergence of the BFGS method with a modified WWP line search for nonconvex functions
Abstract

The BFGS method, which has great numerical stability, is one of the quasi-Newton line search methods. However, the global convergence of the BFGS method with a Wolfe line search is still an open problem for general functions. Recently, Yuan et al. ...

research-article
Proximal algorithm for minimization problems in l0-regularization for nonlinear inverse problems
Abstract

In this paper, we study a proximal method for the minimization problem arising from l0-regularization for nonlinear inverse problems. First of all, we prove the existence of solutions and give an optimality condition for solutions to the ...

research-article
Parareal for index two differential algebraic equations
Abstract

This article proposes modifications of the Parareal algorithm for its application to higher index differential algebraic equations (DAEs). It is based on the idea of applying the algorithm to only the differential components of the equation and ...

research-article
Substructured two-grid and multi-grid domain decomposition methods
Abstract

Two-level Schwarz domain decomposition methods are very powerful techniques for the efficient numerical solution of partial differential equations (PDEs). A two-level domain decomposition method requires two main components: a one-level ...

research-article
A formal construction of a divergence-free basis in the nonconforming virtual element method for the Stokes problem
Abstract

We develop a formal construction of a pointwise divergence-free basis in the nonconforming virtual element method of arbitrary order for the Stokes problem introduced in Zhao et al. (SIAM J. Numer. Anal. 57(6):2730–2759, 2019). The proposed ...

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