Showing papers by "Jun Zhang published in 1996"
TL;DR: A new relaxation analysis and two acceleration schemes are proposed for the five-point red-black Gauss-Seidel smoothing in multigrid for solving a two-dimensional Poisson equation and it is discovered that underrelaxation is applicable to restriction half cycle and overrelaxations are applicable to interpolation half cycle.
43 citations
TL;DR: In this article, the Lanczos @t-method with perturbations proportional to Faber polynomials is employed to approximate the Bessel functions of the first kind J"v(z) and the second kind Y"v (z), the Hankel functions of H"v^(^1^)(z) of integer order v for specific outer regions of the complex plane, i.e. |z| >= R for some R.
9 citations
TL;DR: A novel heuristic residual analysis is proposed to derive a computationally cost-effective residual projection operator in multigrid with the five-point Red-Black Gauss-Seidel relaxation for solving the two-dimensional Poisson equation.
8 citations
TL;DR: In this paper, symbolic representations of the scaled Faber polynomials on any fan-shaped section of the complex plane are used as the perturbation terms in the Lanczos τ-method.
Abstract: This paper is to complete and improve the work reported in [1,2], using the Lanczos τ-method (in Coleman's version) to approximate the Bessel functions Y 0 ( z ) and Y 1 ( z ). We introduce symbolic representations of the scaled Faber polynomials on any fan-shaped section of the complex plane. These Faber polynomials are used as the perturbation terms in the τ-method. Numerical comparison among the power series, the Chebyshev series and the τ-method are conducted to show the accuracy improvement achieved by this new version of the τ-method. Some concluding remarks and suggestions on future research are given.
6 citations
TL;DR: A symbolic computation scheme, based on the Lanczos ?
5 citations