Texas Instruments TI-80, Manual Book

Page: 168 / 235

11-4 Applications
This program uses the Newton-Raphson method to find the roots (zeros) of a
function numerically.
Find the roots of ex
ì
3X.
This program uses the Newton-Raphson method to find a root
of
Y1 based on an initial guess. The program prompts for the
initial guess. One way to make this initial guess is to graph
and trace the function, and then enter X as the guess.
PROGRAM:NEWTON
:INPUT "INITIAL X=",X
Input initial guess.
:LBL N Begin loop.
:X
ì
Y1/NDERIV(Y1,X,X)
→
R Calculate new root.
:DISP R
:PAUSE
:IF ABS (X
ì R)
≤
ABS (X/1 í 10) Test for convergence.
:STOP
:R
→
X
Estimate with new root.
:GOTO N
Follow this procedure to solve the problem.
1. Press
3
and select FUNC .
2. Enter the program.
3. Press
(
. Enter the expression e õì 3X to define Y1 .
4. Graph the function using ZDECIMAL from the ZOOM
menu.
Program: Newton’s Numerical Solve Routine
Problem
Program
Procedure