alg023.txt

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

> restart;
> # NEWTON-RAPHSON ALGORITHM 2.3
> #
> # To find a solution to f(x) = 0 given an
> # initial approximation p0:
> #
> # INPUT:   initial approximation p0; tolerance TOL;
> #          maximum number of iterations NO.
> #
> # OUTPUT:  approximate solution p or a message of failure
> alg023 := proc() local F, FP, OK, P0, TOL, NO, FLAG, NAME, OUP, F0, I, FP0, D;
> printf(`This is Newton's Method\n`);
> printf(`Input the function F(x) in terms of x\n`);
> printf(`For example: cos(x)\n`);
> F := scanf(`%a`)[1];
> FP := unapply(diff(F,x),x);
> F := unapply(F,x);
> OK := FALSE;
> printf(`Input initial approximation\n`);
> P0 := scanf(`%f`)[1]; 
> while OK = FALSE do
> printf(`Input tolerance\n`);
> TOL := scanf(`%f`)[1];
> if TOL <= 0 then
> printf(`Tolerance must be positive\n`);
> else 
> OK := TRUE;
> fi;
> od;
> OK := FALSE;
> while OK = FALSE do
> printf(`Input maximum number of iterations - no decimal point\n`);
> NO := scanf(`%d`)[1];
> if NO <= 0 then
> printf(`Must be positive integer\n`);
> else 
> OK := TRUE;
> fi;
> od;
> if OK = TRUE then
> 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;
> printf(`Select amount of output\n`);
> printf(`1. Answer only\n`);
> printf(`2. All intermediate approximations\n`);
> printf(`Enter 1 or 2\n`);
> FLAG := scanf(`%d`)[1];
> fprintf(OUP, `Newton's Method\n`);
> if FLAG = 2 then
> fprintf(OUP, `  I   P                 F(P)\n`);
> fi;
> F0 := F(P0);
> # Step 1
> I := 1;
> OK := TRUE;
> # Step 2
> while I <= NO and OK = TRUE do  
> # Step 3
> # Compute P(I)
> FP0 := FP(P0);
> D := F0/FP0;
> # Step 6
> P0 := P0 - D;  
> F0 := F(P0);
> if FLAG = 2 then
> fprintf(OUP,`%3d   %14.8e   %14.7e\n`,I,P0,F0);
> fi;
> # Step 4
> if abs(D) < TOL then
> # Procedure completed successfully
> fprintf(OUP,`\nApproximate solution = %12.8f\n`,P0);
> fprintf(OUP,`with F(P) = %.10e\n`,F0);
> fprintf(OUP,`Number of iterations = %d\n`,I);
> fprintf(OUP,`Tolerance = %.10e\n`,TOL);
> OK := FALSE;
> # Step 5
> else
> I := I+1;
> fi;
> od;
> if OK = TRUE then
> # Step 7
> # Procedure completed unsuccessfully
> fprintf(OUP,`\nIteration number %d`,NO);
> fprintf(OUP,` gave approximation %.10e\n`,P0);
> fprintf(OUP,`with F(P) = %.10e not within tolerance  %.10e\n`,F0,TOL);
> fi;
> if OUP <> default then
> fclose(OUP):
> printf(`Output file %s created successfully`,NAME);
> fi;
> fi;
> RETURN(0);
> end;
> alg023();