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).

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

OK := FALSE:

while OK = FALSE do

print(`Choice of input method: `):

print(`1. Input entry by entry from keyboard `):

print(`2. Input data from a text file `):

print(`3. Generate data using a function F `):

print(`Choose 1, 2, or 3 please `):

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

if FLAG = 1 or FLAG = 2 or FLAG = 3 then

OK := TRUE:

fi:

od:

if FLAG = 1 then

OK := FALSE:

while OK <> TRUE do

print(`Input n `):

N := scanf(`%d`)[1]:print(`n = `):print(N):

if N > 0 then

OK := TRUE:

for I1 from 0 to N do

print(`Input X(i) and F(X(i)) for i = `):print(I1):

print(`separated by a space `):

XX[I1] := scanf(`%f`)[1]:

Q[I1,0] := scanf(`%f`)[1]:print(`Entries are`):print(XX[I1],Q[I1,0]):

od:

else

print(`Number must be a positive integer `):

fi:

od:

fi:

if FLAG = 2 then

print(`Has a text file been created with the data in two columns ? `):

print(`Enter Y or N `):

A := scanf(` %c`)[1]:print(`Entry = `):print(A):

if A = "Y" or A = "y" then

print(`Input the file name in the form - `):

print(`drive:\134 ame.ext `):

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

NAME := scanf(`%s`)[1]:print(`Entry = `):print(NAME):

INP := fopen(NAME,READ,TEXT):

OK := FALSE:

while OK = FALSE do

print(`Input N `):

N := scanf(`%d`)[1]:print(`n = `):print(N):

if N > 0 then

for I1 from 0 to N do

XX[I1] := fscanf(INP, `%f`)[1]:

Q[I1,0] := fscanf(INP, `%f`)[1]:

od:

fclose(INP):

OK := TRUE:

else

print(`Number must be a positive integer `):

fi:

od:

else

print(`Please create the input file in two column `):

print(`form with the X values and `):

print(`F(X) values in the corresponding columns. `):

print(`The program will end so the input file can `):

print(`be created. `):

OK := FALSE:

fi:

if FLAG = 3 then

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

print(`For example: cos(x) `):

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

F := unapply(F,x):

OK := FALSE:

while OK = FALSE do

print(`Input n `):

N := scanf(`%d`)[1]:print(`n = `):print(N):

if N > 0 then

for I1 from 0 to N do

print(`Input X(i) for i = `):print(I1):

XX[I1] := scanf(`%f`)[1]:print(`Entry = `):print(XX[I1]):

Q[I1,0] := F(XX[I1]):

od:

OK := TRUE:

else

print(`Number must be a positive integer `):

fi:

od:

fi:

if OK = TRUE then

print(`Input the point at which the polynomial is to be evaluated `):

X := scanf(`%f`)[1]:print(`Value = `):print(X):

fi:

if OK = TRUE then

# Step 1

D1[0] := evalf(X-XX[0]):

for I1 from 1 to N do

D1[I1] := evalf(X-XX[I1]):

for J from 1 to I1 do

Q[I1,J] := evalf((D1[I1]*Q[I1-1,J-1]-D1[I1-J]*Q[I1,J-1])/(D1[I1]-D1[I1-J])):

od:

# Step 2

print(`Select output destination `):

print(`1. Screen `):

print(`2. Text file `):

print(`Enter 1 or 2 `):

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

if FLAG = 2 then

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

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

NAME := scanf(`%s`)[1]:

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

else

OUP := default:

fi:

fprintf(OUP, `NEVILLE'S METHOD\134n `):

fprintf(OUP, `Table for P evaluated at X = %12.8f , follows: \134n`, X):

fprintf(OUP, `Entries are XX(I), Q(I,0), ..., Q(I,I) `):

fprintf(OUP, `for each I = 0, ..., N where N = %3d\134n\134n`, N):

for I1 from 0 to N do

fprintf(OUP, `%11.8f `, XX[I1]):

for J from 0 to I1 do

fprintf(OUP, `%11.8f `, Q[I1,J]):

od:

fprintf(OUP, `\134n`):

od:

if OUP <> default then

fclose(OUP):

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

fi:

STxUaGlzfmlzfk5ldmlsbGUnc35NZXRob2QufCt+RzYi

STlDaG9pY2V+b2Z+aW5wdXR+bWV0aG9kOn5HNiI=

SUcxLn5JbnB1dH5lbnRyeX5ieX5lbnRyeX5mcm9tfmtleWJvYXJkfkc2Ig==

SUAyLn5JbnB1dH5kYXRhfmZyb21+YX50ZXh0fmZpbGV+RzYi

SUUzLn5HZW5lcmF0ZX5kYXRhfnVzaW5nfmF+ZnVuY3Rpb25+Rn5HNiI=

STpDaG9vc2V+MSx+Mix+b3J+M35wbGVhc2V+RzYi

SSlFbnRyeX49fkc2Ig==

IiIi

SSlJbnB1dH5ufkc2Ig==

SSVufj1+RzYi

IiIk

SUBJbnB1dH5YKGkpfmFuZH5GKFgoaSkpfmZvcn5pfj1+RzYi

IiIh

STZzZXBhcmF0ZWR+Ynl+YX5zcGFjZX5HNiI=

SSxFbnRyaWVzfmFyZUc2Ig==

NiQkIiM1ISIiJCIoeD5sKCEiKA==

SUBJbnB1dH5YKGkpfmFuZH5GKFgoaSkpfmZvcn5pfj1+RzYi

IiIi

STZzZXBhcmF0ZWR+Ynl+YX5zcGFjZX5HNiI=

SSxFbnRyaWVzfmFyZUc2Ig==

NiQkIiM4ISIiJCIoZzM/JyEiKA==

SUBJbnB1dH5YKGkpfmFuZH5GKFgoaSkpfmZvcn5pfj1+RzYi

IiIj

STZzZXBhcmF0ZWR+Ynl+YX5zcGFjZX5HNiI=

SSxFbnRyaWVzfmFyZUc2Ig==

NiQkIiM7ISIiJCIoQVNiJSEiKA==

SUBJbnB1dH5YKGkpfmFuZH5GKFgoaSkpfmZvcn5pfj1+RzYi

IiIk

STZzZXBhcmF0ZWR+Ynl+YX5zcGFjZX5HNiI=

SSxFbnRyaWVzfmFyZUc2Ig==

NiQkIiM+ISIiJCIoJz09RyEiKA==

SWZuSW5wdXR+dGhlfnBvaW50fmF0fndoaWNofnRoZX5wb2x5bm9taWFsfmlzfnRvfmJlfmV2YWx1YXRlZH5HNiI=

SSlWYWx1ZX49fkc2Ig==

JCIjOiEiIg==

STtTZWxlY3R+b3V0cHV0fmRlc3RpbmF0aW9ufkc2Ig==

SSsxLn5TY3JlZW5+RzYi

SS4yLn5UZXh0fmZpbGV+RzYi

SS5FbnRlcn4xfm9yfjJ+RzYi

SSlFbnRyeX49fkc2Ig==

IiIi

NEVILLE'S METHOD Table for P evaluated at X = 1.50000000 , follows: Entries are XX(I), Q(I,0), ..., Q(I,I) for each I = 0, ..., N where N = 3 1.00000000 0.76519770 1.30000000 0.62008600 0.52334487 1.60000000 0.45540220 0.51029680 0.51247148 1.90000000 0.28181860 0.51326340 0.51128567 0.51181269

JSFH