Q: Clenshaw Recurrence Formula

[Tilo Schwarz]

NOTE: FOLLOWUPS TO SCI.MATH.NUM-ANALYSIS

Hello everybody,

in the 'Numerical Recipes' I read about the 'Clenshaw Recurrence Formula'. It
t is used to calculate
a sum

f(x) = sum_{k=0}^N c_k F_k(x)

efficiently, where F_k(x) is a real Funktion, which obeys the recurrence
ation

F_{n+1} = a(n,x) F_n(x) + b(n,x) F_{n-1}(x) .

I was wondering, if there exists a equivalent formula, if F_k(x) is a vector
- valued Funktion in R^n taking an n-dimensional vector as argument and
n,x) is a matrix.

Thanks for any hints...

Bye
Tilo

--------------------
Tilo Schwarz, Daimler-Benz AG, Research Center Ulm, FT3/AB
Address: Wilhelm-Runge-Str.11, P.O. Box 23 60, 89013 Ulm, Germany
Phone: +49 731 505 2376
Email: tilo.s...@dbag.ulm.daimlerbenz.com
(NeXT- and MIME-Mail welcome)

[Bernard Danloy]

In article <72pd0j$f...@news.sns-felb.debis.de>,
tilo.s...@dbag.ulm.DaimlerBenz.COM (Tilo Schwarz) wrote :

: NOTE: FOLLOWUPS TO SCI.MATH.NUM-ANALYSIS

It is clear for me that the Clenshaw technique can be extended to matrix
recurrences but i never saw a specific paper on the subject ; can you
explain your problem in more details or e-mail me ?

Bernard Danloy