CHEBYSHEV RATIONAL APPROXIMATION ALGORITHM
*
* To obtain the rational approximation
*
* rT(x) = (p0*T0 + p1*T1 +...+ Pn*Tn) / (q0*T0 + q1*T1 +...+ qm*Tm)
*
* for a given function f(x):
*
* INPUT nonnegative integers m and n.
*
* OUTPUT coefficients q0, q1, ... , qm, p0, p1, ... , pn.
*
* The coefficients of the Chebyshev expansion a0, a1, ... could
* be calculated instead of input as is assumed in this program.
FAST
FOURIER TRANSFORM ALGORITHM
* To compute the coefficients in the discrete approximation
* for the data (x(J),y(J)), 0<=J<=2m-1 where m=2**p and
* x(J)=-pi+J*pi/m for 0<=J<=2m-1.
*
* INPUT: m; y(0),y(1),...y(2m-1).
*
* OUTPUT: complex numbers c(0),...,c(2m-1); real numbers
* a(0),...,a(m); b(1),...,b(m-1).
*
* NOTE: The multiplication by EXP(-K*PI*I) is done within the
* program.
PADE'
RATIONAL APPROXIMATION ALGORITHM
*
* To obtain the rational approximation
*
* r(x) = p(x) / q(x)
* = (p0 + p1*x + ... + Pn*x^n) / (q0 + q1*x + ... + qm*x^m)
*
* for a given function f(x):
*
* INPUT nonnegative integers m and n.
*
* OUTPUT coefficients q0, q1, ... , qm, p0, p1, ... , pn.