(12C) Secant Method solution of f(x)=0

[Csaba Tizedes]

A little idea, because I hate to calculate the next estimated root. (A BIG HINT: With this method you can easily implement Muller's method if your calculator include parabolic fit!!!)

For secant method here is a "skeleton", but it can be run:

Code:

0
x^,r
STO 0
RCL 8
y^,r
LSTx
SUM-
RCL 7
STO 8
RCL 0
STO 7
PSE    // removable, you can see here the actual estimation of the root
-----------
e^x    // f(x)=0 here, eg: e^x=x^2
LSTx
ENTER
×
-
RCL 0
SUM+

Usage similar as above:

1. but first clear the stat regs: CLEAR SUM,
2. then store x0 into R7
3. estimate f(x0) and store x0, f(x0) point into stat regs: f(x0) ENTER x0 SUM+
4. then store x1 into R8
5. estimate f(x1) and store x1, f(x1) point into stat regs: f(x1) ENTER x1 SUM+
6. jump to the beginning of the program memory and run the program: CLEAR PRGM R/S
7. the estimations shows on the display
8. the approximated root is in R0
9. (during testing I got Error 2 sometimes...)
   

For e^x=x^2:

1. f CLEAR SUM
2. 0 STO R7
3. 1 ENTER 0 SUM+
4. 1 STO 8
5. 1.7 ENTER 1 SUM+
6. f CLEAR PRGM
7. R/S
   

The result:

Code:

-1.4286  R/S
-0.5100  R/S
-0.6560  R/S
-0.7074  R/S
-0.7034  R/S
-0.7035  R/S
-0.7035  R/S
...

Csaba