Download:
|
by Jun Zhang
z), Computers Math. Applic
http://www.cs.engr.uky.edu/~jzhang/pub/BESSEL/note.ps.gz
Add To MetaCart
Abstract:
This paper is to complete and improve the work reported in [1, 2], using the Lanczos-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-method. Numerical comparison among the power series, the Chebyshev series and the-method are conducted to show the accuracy improvement achieved by this new version of the-method. Some concluding remarks and suggestions on future research are given. Key words and phrases. Automated-method, symbolic Faber polynomials, Chebyshev series, Bessel functions.
Citations
|
21
|
A study of semiiterative methods for nonsymmetric systems of linear equations
– Eiermann, Niethammer, et al.
- 1985
|
|
18
|
On semiiterative methods generated by Faber polynomials
– Eiermann
- 1989
|
|
14
|
A hybrid Arnoldi-Faber iterative method for nonsymmetric systems of linear equations
– Starke, Varga
- 1993
|
|
5
|
The Faber polynomials for annular sectors
– Coleman, Myers
- 1995
|
|
4
|
Faber polynomials for circular sectors
– Coleman, Smith
- 1987
|
|
4
|
Computation of Faber series with application to numerical polynomial approximation in the complex plane
– Ellacott
- 1983
|
|
4
|
On the Faber transformation and efficient numerical rational approximation
– ELLACOTT
- 1983
|
|
4
|
Chebyshev Series for Mathematical Functions
– Clenshaw
- 1962
|
|
3
|
Explicit Faber polynomials on circular sectors
– Gatermann, Hoffmann, et al.
- 1992
|
|
3
|
The Faber polynomials for circular arcs, in Mathematics of Computation 1943--1993: a half-century of computational mathematics
– He
- 1993
|
|
3
|
Polynomial approximations in the complex plane
– Coleman
- 1987
|
|
3
|
Complex polynomial approximations by the Lanczos -method: Dawson's integral
– Coleman
- 1987
|
|
2
|
A Faber series approach to cardinal interpolation
– Chui, Stockler, et al.
- 1992
|
|
2
|
The construction of Chebyshev approximations in the complex plane
– Elliott
- 1978
|
|
2
|
On Clenshaw's method and a generalization to Faber series
– Ellacott
- 1988
|
|
2
|
Computing with the Faber transform, in Rational Approximation and Interpolation
– Ellacott, Saff
- 1984
|
|
2
|
The Lanczos tau-method
– Coleman
- 1976
|
|
1
|
A numerical method for the computation of Faber polynomials for starlike domains
– Papamichael, Soares, et al.
- 1993
|
|
1
|
Chebyshev expansions for the Bessel function J n (z) in the complex plane
– Coleman, Monaghan
- 1983
|
|
1
|
Chebyshev series approximations for the Bessel function Y n (z) with complex argument
– Belward, Zhang
|
