Numerical Algorithms

The aim of this paper is to introduce a fast and efficient new two-grid method to solve the d-dimensional (d=1,2,3) Poisson elliptic equations. The finite difference equations at all interior grid points form a large sparse linear system, which needs to ...

The present study is an attempt to extend Barzilai and Borwein's method for dealing with unconstrained single objective optimization problems to multiobjective ones. As compared with Newton, Quasi-Newton and steepest descent multi-objective optimization ...

We introduce the G-blossom of a polynomial by altering the diagonal property of the classical blossom, replacing the identity function by arbitrary linear functions G=G(t). By invoking the G-blossom, we construct G-Bernstein bases and G-Bézier curves ...

In this paper we present a new steepest-descent type algorithm for convex optimization problems. Our algorithm pieces the unknown into sub-blocs of unknowns and considers a partial optimization over each sub-bloc. In quadratic optimization, our method ...

The present paper is concerned with theoretical properties of the modified Newton-HSS method for large sparse non-Hermitian positive definite systems of nonlinear equations. Assuming that the nonlinear operator satisfies the Hölder continuity condition, ...

In this paper, a numerical method with second order temporal accuracy and fourth order spatial accuracy is developed to solve a anomalous subdiffusion equation; by Fourier analysis, the convergence, stability and solvability of the numerical method are ...

We propose a smooth fictitious domain/multiresolution method for enhancing the accuracy order in solving second order elliptic partial differential equations on general bivariate domains. We prove the existence and uniqueness of the solution of a ...

The Quadratic Eigenvalue Complementarity Problem (QEiCP) is an extension of the Eigenvalue Complementarity Problem (EiCP) that has been introduced recently. Similar to the EiCP, the QEiCP always has a solution under reasonable hypotheses on the matrices ...

In this paper, we consider two types of space-time fractional diffusion equations(STFDE) on a finite domain. The equation can be obtained from the standard diffusion equation by replacing the second order space derivative by a Riemann-Liouville ...

In this paper, we improve the convergence theorem in the paper by Yang (Journal of Industrial and Management Optimization 1, 211---217, 2005), and propose a new modified convergence theorem. The theorem and the proof presented in the present paper are ...

This article provides an overview of some of the mathematical principles of Automatic Differentiation (AD). In particular, we summarise different descriptions of the Forward Mode of AD, like the matrix-vector product based approach, the idea of lifting ...

For non-Hermitian saddle point linear systems, Pan, Ng and Bai presented a positive semi-definite and skew-Hermitian splitting (PSS) preconditioner (Pan et al. Appl. Math. Comput. 172, 762---771 2006), to accelerate the convergence rate of the Krylov ...