Recent ADI iteration analysis and results

Conference · Sat Dec 31 04:00:00 EST 1994

OSTI ID:223864

Wachspress, E L

Some recent ADI iteration analysis and results are discussed. Discovery that the Lyapunov and Sylvester matrix equations are model ADI problems stimulated much research on ADI iteration with complex spectra. The ADI rational Chebyshev analysis parallels the classical linear Chebyshev theory. Two distinct approaches have been applied to these problems. First, parameters which were optimal for real spectra were shown to be nearly optimal for certain families of complex spectra. In the linear case these were spectra bounded by ellipses in the complex plane. In the ADI rational case these were spectra bounded by {open_quotes}elliptic-function regions{close_quotes}. The logarithms of the latter appear like ellipses, and the logarithms of the optimal ADI parameters for these regions are similar to the optimal parameters for linear Chebyshev approximation over superimposed ellipses. W.B. Jordan`s bilinear transformation of real variables to reduce the two-variable problem to one variable was generalized into the complex plane. This was needed for ADI iterative solution of the Sylvester equation.

• Research Organization: Front Range Scientific Computations, Inc., Boulder, CO (United States); USDOE, Washington, DC (United States); National Science Foundation, Washington, DC (United States)
• OSTI ID: 223864
• Report Number(s): CONF-9404305--Vol.1; ON: DE96005735
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
COMPLEX MANIFOLDS
ITERATIVE METHODS
LYAPUNOV METHOD
MATRICES