Web pdp-10.trailing-edge.com

Trailing-Edge - PDP-10 Archives - decuslib10-02 - 43,50145/tcsp.doc
There are 2 other files named tcsp.doc in the archive. Click here to see a list.
```SUBROUTINE TCSP

PURPOSE
A SERIES EXPANSION IN SHIFTED CHEBYSHEV POLYNOMIALS WITH
INDEPENDENT VARIABLE X IS TRANSFORMED TO A POLYNOMIAL WITH
INDEPENDENT VARIABLE Z, WHERE X=A*Z+B.

USAGE
CALL TCSP(A,B,POL,N,C,WORK)

DESCRIPTION OF PARAMETERS
A	 - FACTOR OF LINEAR TERM IN GIVEN LINEAR TRANSFORMATION
B	 - CONSTANT TERM IN GIVEN LINEAR TRANSFORMATION
POL	 - COEFFICIENT VECTOR OF POLYNOMIAL (RESULTANT VALUE)
COEFFICIENTS ARE ORDERED FROM LOW TO HIGH
N	 - DIMENSION OF COEFFICIENT VECTORS POL AND C
C	 - GIVEN COEFFICIENT VECTOR OF EXPANSION
COEFFICIENTS ARE ORDERED FROM LOW TO HIGH
POL AND C MAY BE IDENTICALLY LOCATED
WORK  - WORKING STORAGE OF DIMENSION 2*N

REMARKS
COEFFICIENT VECTOR C REMAINS UNCHANGED IF NOT COINCIDING
WITH COEFFICIENT VECTOR POL.
OPERATION IS BYPASSED IN CASE N LESS THAN 1.
THE LINEAR TRANSFORMATION X=A*Z+B OR Z=(1/A)(X-B) TRANSFORMS
THE RANGE (0,1) IN X TO THE RANGE (ZL,ZR) IN Z, WHERE
ZL=-B/A AND ZR=(1-B)/A.
FOR GIVEN ZL, ZR WE HAVE A=1/(ZR-ZL) AND B=-ZL/(ZR-ZL).

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
NONE

METHOD
THE TRANSFORMATION IS BASED ON THE RECURRENCE EQUATION FOR
SHIFTED CHEBYSHEV POLYNOMIALS TS(N,X)
TS(N+1,X)=(4*X-2)*TS(N,X)-TS(N-1,X),
WHERE THE FIRST TERM IN BRACKETS IS THE INDEX,
THE SECOND IS THE ARGUMENT.
STARTING VALUES ARE TS(0,X)=1, TS(1,X)=2*X-1.
THE TRANSFORMATION IS IMPLICITLY DEFINED BY MEANS OF
X=A*Z+B TOGETHER WITH
SUM(POL(I)*Z**(I-1), SUMMED OVER I FROM 1 TO N)
=SUM(C(I)*TS(I-1,X), SUMMED OVER I FROM 1 TO N).
```