restart:

# FIXED-POINT ALGORITHM 2.2

# To find a solution to p = g(p) given an

# initial approximation p0

# INPUT: initial approximation p0: tolerance TOL:

# maximum number of iterations NO.

# OUTPUT: approximate solution p or

# a message that the method fails.

print(`This is the Fixed-Point Method.\134n`):

print(`Input the function G(x) in terms of x\134n`):

print(`For example: cos(x)\134n`):

G := scanf(`%a`)[1]:print(G):

G := unapply(G,x):

OK := FALSE:

print(`Input initial approximation\134n`):

P0 := scanf(`%f`)[1]: print(`Initial approximation = `):print(P0):

while OK = FALSE do

print(`Input tolerance\134n`):

TOL := scanf(`%f`)[1]:print(`Tolerance = `):print(TOL):

if TOL <= 0 then

print(`Tolerance must be positive\134n`):

else

OK := TRUE:

fi:

od:

OK := FALSE:

while OK = FALSE do

print(`Input maximum number of iterations - no decimal point\134n`):

NO := scanf(`%d`)[1]:print(`Maximum number of iterations = `):print(N0):

if NO <= 0 then

print(`Must be positive integer\134n`):

else

OK := TRUE:

fi:

od:

if OK = TRUE then

print(`Select output destination\134n`):

print(`1. Screen\134n`):

print(`2. Text file\134n`):

print(`Enter 1 or 2\134n`):

FLAG := scanf(`%d`)[1]:print(`Entry = `):print(FLAG):

if FLAG = 2 then

print(`Input the file name in the form - drive:\134\134name.ext\134n`):

print(`For example: A:\134\134OUTPUT.DTA\134n`):

NAME := scanf(`%s`)[1]:print(`File name is `):print(NAME):

OUP := fopen(NAME,WRITE,TEXT):

else

OUP := default:

fi:

print(`Select amount of output\134n`):

print(`1. Answer only\134n`):

print(`2. All intermediate approximations\134n`):

print(`Enter 1 or 2\134n`):

FLAG := scanf(`%d`)[1]:print(`Entry = `):print(FLAG):

fprintf(OUP, `FIXED-POINT METHOD\134n`):

if FLAG = 2 then

fprintf(OUP, ` I P\134n`):

fi:

# Step 1

I1 := 1:

OK := TRUE:

# Step 2

while I1 <= NO and OK = TRUE do

# Step 3

# Compute P(I)

P := G(P0):

if FLAG = 2 then

fprintf(OUP, `%3d %15.8e\134n`, I1, P):

fi:

# Step 4

if abs(P-P0) < TOL then

# Procedure completed successfully

fprintf(OUP, `\134nApproximate solution P = %12.8f\134n`, P):

fprintf(OUP, `Number of iterations = %3d`, I1):

fprintf(OUP, ` Tolerance = %14.8e\134n`,TOL):

OK := FALSE:

else

# Step 5

I1 := I1+1:

# Step 6

# Update P0

P0 := P:

fi:

od:

if OK = TRUE then

# Step 7

# Procedure completed unsuccessfully

fprintf(OUP, `\134nIteration number %3d`, NO):

fprintf(OUP, ` gave approximation %12.8f\134n`, P):

fprintf(OUP, `not within tolerance %14.8e\134n`,TOL):

fi:

if OUP <> default then

fclose(OUP):

print(`Output file `,NAME,` created successfully`):

fi:

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IiIi

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SS5FbnRlcn4xfm9yfjJ8K0c2Ig==

SSlFbnRyeX49fkc2Ig==

IiIj

FIXED-POINT METHOD I P 1 1.34839972e+00 2 1.36737637e+00 3 1.36495702e+00 4 1.36526475e+00 Approximate solution P = 1.36526475 Number of iterations = 4 Tolerance = 5.00000000e-04

JSFH