A generalized cyclic iterative method for solving variational inequalities over the solution set of a split common fixed point problem
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.
Improved two-step Newton’s method for computing simple multiple zeros of polynomial systems
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 ...
A class of C2 quasi-interpolating splines free of Gibbs phenomenon
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 ...
Linear and nonlinear substructured Restricted Additive Schwarz iterations and preconditioning
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 ...
On the rational approximation of Markov functions, with applications to the computation of Markov functions of Toeplitz matrices
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 ...
Adaptive three-term PRP algorithms without gradient Lipschitz continuity condition for nonconvex functions
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 ...
A new family of hybrid three-term conjugate gradient methods with applications in image restoration
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 ...
An adaptive mesh refinement method for indirectly solving optimal control problems
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 ...
Generalized second derivative linear multistep methods for ordinary differential equations
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 ...
In reference to a self-referential approach towards smooth multivariate approximation
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) ...
A variant of PMHSS iteration method for a class of complex symmetric indefinite linear systems
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 ...
A second-order dynamical system for equilibrium problems
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 ...
Proximal algorithm for minimization problems in l0-regularization for nonlinear inverse problems
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 ...
Parareal for index two differential algebraic equations
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 ...
Substructured two-grid and multi-grid domain decomposition methods
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 ...
A formal construction of a divergence-free basis in the nonconforming virtual element method for the Stokes problem
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 ...