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

print(`This is Newton's Method\134n`):

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

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

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

FP := unapply(diff(F,x),x):

F := unapply(F,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`):

N0 := scanf(`%d`)[1]:print(`Mximum number of iterations = `):print(N0):

if N0 <= 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]:

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, `Newton's Method\134n`):

if FLAG = 2 then

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

fi:

F0 := F(P0):

# Step 1

I1 := 1:

OK := TRUE:

# Step 2

while I1 <= N0 and OK = TRUE do

# Step 3

# Compute P(I)

FP0 := FP(P0):

D1 := F0/FP0:

# Step 6

P0 := P0 - D1:

F0 := F(P0):

if FLAG = 2 then

fprintf(OUP,`%3d %14.8e %14.7e\134n`,I1,P0,F0):

fi:

# Step 4

if abs(D1) < TOL then

# Procedure completed successfully

fprintf(OUP,`\134nApproximate solution = %12.8f\134n`,P0):

fprintf(OUP,`with F(P) = %.10e\134n`,F0):

fprintf(OUP,`Number of iterations = %d\134n`,I1):

fprintf(OUP,`Tolerance = %.10e\134n`,TOL):

OK := FALSE:

# Step 5

else

I1 := I1+1:

fi:

od:

if OK = TRUE then

# Step 7

# Procedure completed unsuccessfully

fprintf(OUP,`\134nIteration number %d`,N0):

fprintf(OUP,` gave approximation %.10e\134n`,P0):

fprintf(OUP,`with F(P) = %.10e not within tolerance %.10e\134n`,F0,TOL):

fi:

if OUP <> default then

fclose(OUP):

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

fi:

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SUdJbnB1dH50aGV+ZnVuY3Rpb25+Rih4KX5pbn50ZXJtc35vZn54fCtHNiI=

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LCYtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kieEdGKCIiIkYqISIi

ST1JbnB1dH5pbml0aWFsfmFwcHJveGltYXRpb258K0c2Ig==

STlJbml0aWFsfmFwcHJveGltYXRpb25+PX5HNiI=

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ST9NeGltdW1+bnVtYmVyfm9mfml0ZXJhdGlvbnN+PX5HNiI=

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SSsxLn5TY3JlZW58K0c2Ig==

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SSlFbnRyeX49fkc2Ig==

IiIi

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SSlFbnRyeX49fkc2Ig==

IiIj

Newton's Method I P F(P) 1 7.39536134e-01 -7.5487470e-04 2 7.39085178e-01 -7.5100000e-08 Approximate solution = 0.73908518 with F(P) = -7.5100000000e-08

Number of iterations = 2 Tolerance = 5.0000000000e-04

JSFH