E-CodeNewton's method with an iteration table — a TI-84 Plus CE program
NEWTTBL is a TI-BASIC program for the TI-84 Plus CE. Type any f(X) and a starting guess: prints every Newton iterate in a table (central-difference derivative), then the root to 9 decimals, f(root) and the iteration count; reports a flat spot, divergence or no convergence.
What it asks for and what it shows
It asks for 2 values at its prompts. In the example below it shows X, ITERATIONS, 1 , 2 , 3 .
Example run
One of its oracle test cases: “x^3-2x-5 from 2”. The inputs are typed in order, and the results are the values the case expects on the screen.
| Step | Value |
|---|---|
| You enter | |
| Input 1 | X^3-2X-5 |
| Input 2 | 2 |
| The screen shows | |
X= | 2.094551482 |
ITERATIONS= | 4 |
1 | 2.1 |
2 | 2.094568 |
3 | 2.094551 |
How it's checked
7 test cases, each checked against an independent method. Replayed key by key on a virtual TI-84 Plus CE, they make 41 checks.
How E-Code checks every program
Run it or put it on your calculator
- Open the library in the TI-84 Plus CE calculator and pick “Newton's method with an iteration table” (NEWTTBL).
- Put it on your own calculator with a computer and a USB cable, or type it in by hand.
Related programs
- Newton-Raphson root finder
- Bisection root finder
- Numerical integration lab
- ODE solver: Euler vs RK4 with a table
- Quadratic formula solver
All TI-84 Plus CE math programs · All TI-84 Plus CE programs