alg031.txt

Numerical Anaysis 8th Edition Burden and Faires (Maple Source)

> restart;
> # NEVILLE'S ITERATED INTERPOLATION ALGORITHM 3.1
> #
> # To evaluate the interpolating polynomial P on the
> # (n+1) distinct numbers x(0), ..., x(n) at the number x
> # for the function f:
> #
> # INPUT:   numbers x(0),..., x(n) as XX(0),...,XX(N);
> #          number x; values of f as the first column of Q
> #          or may be computed if function f is supplied.
> #
> # OUTPUT:  the table Q with P(x) = Q(N+1,N+1).
> alg031 := proc() local TRUE, FALSE, OK, FLAG, N, I, XX, Q, A, NAME, INP, F, X, D, J, OUP;
> printf(`This is Neville's Method.\n`);
> OK := FALSE;
> while OK = FALSE do
> printf(`Choice of input method:\n`);
> printf(`1. Input entry by entry from keyboard\n`);
> printf(`2. Input data from a text file\n`);
> printf(`3. Generate data using a function F\n`);
> printf(`Choose 1, 2, or 3 please\n`);
> FLAG := scanf(`%d`)[1];
> if FLAG = 1 or FLAG = 2 or FLAG = 3 then
> OK := TRUE;
> fi;
> od;
> if FLAG = 1 then
> OK := FALSE;
> while OK <> TRUE do
> printf(`Input n\n`);
> N := scanf(`%d`)[1];
> if N > 0 then
> OK := TRUE;
> for I from 0 to N do
> printf(`Input X(%d) and F(X(%d)) `, I, I);
> printf(`separated by a space\n`);
> XX[I] := scanf(`%f`)[1];
> Q[I,0] := scanf(`%f`)[1];
> od;
> else
> printf(`Number must be a positive integer\n`);
> fi;
> od;
> fi;
> if FLAG = 2 then
> printf(`Has a text file been created with the data in two columns ?\n`);
> printf(`Enter Y or N\n`);
> A := scanf(`\n%c`)[1];
> if A = "Y" or A = "y" then
> printf(`Input the file name in the form - `);
> printf(`drive:\\name.ext\n`);
> printf(`For example:   A:\\DATA.DTA\n`);
> NAME := scanf(`%s`)[1];
> INP := fopen(NAME,READ,TEXT);
> OK := FALSE;
> while OK = FALSE do
> printf(`Input N\n`);
> N := scanf(`%d`)[1];
> if N > 0 then
> for I from 0 to N do
> XX[I] := fscanf(INP, `%f`)[1];
> Q[I,0] := fscanf(INP, `%f`)[1];
> od;
> fclose(INP);
> OK := TRUE;
> else
> printf(`Number must be a positive integer\n`);
> fi;
> od;
> else
> printf(`Please create the input file in two column `);
> printf(`form with the X values and\n`);
> printf(`F(X) values in the corresponding columns.\n`);
> printf(`The program will end so the input file can `);
> printf(`be created.\n`);
> OK := FALSE;
> fi;
> fi;
> if FLAG = 3 then
> printf(`Input the function F(x) in terms of x\n`);
> printf(`For example: cos(x)\n`);
> F := scanf(`%a`)[1];
> F := unapply(F,x);
> OK := FALSE;
> while OK = FALSE do
> printf(`Input n\n`);
> N := scanf(`%d`)[1];
> if N > 0 then
> for I from 0 to N do
> printf(`Input X(%d)\n`, I);
> XX[I] := scanf(`%f`)[1];
> Q[I,0] := F(XX[I]);
> od;
> OK := TRUE;
> else
> printf(`Number must be a positive integer\n`);
> fi;
> od;
> fi;
> if OK = TRUE then
> printf(`Input the point at which the polynomial is to be evaluated\n`);
> X := scanf(`%f`)[1];
> fi;
> if OK = TRUE then
> # Step 1
> D[0] := evalf(X-XX[0]);
> for I from 1 to N do
> D[I] := evalf(X-XX[I]);
> for J from 1 to I do
> Q[I,J] := evalf((D[I]*Q[I-1,J-1]-D[I-J]*Q[I,J-1])/(D[I]-D[I-J]));
> od;
> od;
> # Step 2
> printf(`Select output destination\n`);
> printf(`1. Screen\n`);
> printf(`2. Text file\n`);
> printf(`Enter 1 or 2\n`);
> FLAG := scanf(`%d`)[1];
> if FLAG = 2 then
> printf(`Input the file name in the form - drive:\\name.ext\n`);
> printf(`For example:   A:\\OUTPUT.DTA\n`);
> NAME := scanf(`%s`)[1];
> OUP := fopen(NAME,WRITE,TEXT);
> else
> OUP := default;
> fi;
> fprintf(OUP, `NEVILLE'S METHOD\n`);
> fprintf(OUP, `Table for P evaluated at X = %12.8f , follows: \n`, X);
> fprintf(OUP, `Entries are XX(I), Q(I,0), ..., Q(I,I) `);
> fprintf(OUP, `for each I = 0, ..., N where N = %3d\n\n`, N); 
> for I from 0 to N do
> fprintf(OUP, `%11.8f `, XX[I]);
> for J from 0 to I do
> fprintf(OUP, `%11.8f `, Q[I,J]);
> od;
> fprintf(OUP, `\n`);
> od;
> if OUP <> default then
> fclose(OUP);
> printf(`Output file %s created successfully`,NAME);
> fi;
> fi;
> RETURN(0);
> end;
> alg031();