A fast procedure solving Kepler's equation for elliptic case

The bisection method was applied to localize a solution of Kepler's equation in an extended form where the Newton-Raphson and some other methods are not always stable. This localizer was combined with a variation of the Newton-Raphson method where trigonometric functions are evaluated by Taylor series expansions. As a result, we developed a procedure solving the extended Kepler's equation. It is roughly twice as fast as Halley's method and more for other existing schemes. This significantly speeds up Encke's method applied to orbital elements (Fukushima 1996a). Also, even in solving the original Kepler's equation, it is 20% faster than the author's former method (Fukushima 1996b). (C) 1996 American Astronomical Society.