> restart;
> # STEFFENSEN'S ALGORITHM 2.6
> #
> # To find a solution to g(x) = x
> # given an initial approximation p0:
> #
> # INPUT:   initial approximation p0; tolerance TOL;
> #          maximum number of iterations N0.
> #
> # OUTPUT:  approximate solution p or
> #          a message that the method fails.
> alg026 := proc() local G, OK, P0, TOL, NO, FLAG, NAME, OUP, I, P1, P2, D, P;
> printf(`This is Steffensens Method.\n`);
> printf(`Input the function G(x) in terms of x\n`);
> printf(`For example: cos(x)\n`);
> G := scanf(`%a`)[1];
> G := unapply(G,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, `STEFFENSEN'S METHOD\n`);
> if FLAG = 2 then
> fprintf(OUP, `  I    P\n`);
> fi;
> # Step 1
> I := 1;
> OK := TRUE;
> # Step 2
> while I <= NO and OK = TRUE do
> # Step 3
> # Compute P(1) with superscript (I-1)
> P1 := G(P0);
> # Compute P(2) with superscript (I-1)
> P2 := G(P1);
> if abs(P2-2*P1+P0) < 1.0e-20 then
> FLAG := 1;
> D := 10;
> fprintf(OUP,`Denominator = 0, method fails\n`);
> fprintf(OUP,`best possible is P2(%2d) = %15.8f\n`,I,P2);
> OK := FALSE;
> else
> D := (P1-P0)*(P1-P0)/(P2-2*P1+P0);
> fi;
> # Compute P(0) with superscript (I)
> P := P0-D;
> if FLAG = 2 then
> fprintf(OUP, `%3d%15.8e\n`, I, P);
> fi;
> # Step 4
> if abs(D) < TOL then
> # Procedure completed successfully
> fprintf(OUP, `\nApproximate solution := %12.8f\n`, P);
> fprintf(OUP, `Number of iterations := %3d`, I);
> fprintf(OUP, ` Tolerance := %15.8e\n`,TOL);
> OK := FALSE;
> else
> # Step 5
> I := I+1;
> # Step 6
> # Update P0
> P0 := P;
> fi;
> od;
> if OK = TRUE then
> # Step 7
> # Procedure completed unsuccessfully
> fprintf(OUP, `\nIteration number %3d`, NO);
> fprintf(OUP, ` gave approximation %12.8f\n`, P);
> fprintf(OUP, `not within tolerance %14e\n`,TOL);
> fi;
> if OUP <> default then
> fclose(OUP):
> printf(`Output file %s created successfully`,NAME);
> fi;
> fi;
> RETURN(0);
> end;
> alg026();