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+--- Thread: Recommend root-finder for HP 67 (/thread-14073.html)
Recommend root-finder for HP 67 - Trond - 11-29-2019 06:19 PM
I don't particularly like the root finder from the HP 67 standard pac. I have to insert the program lines into the other code, and it gets stuck frequently it seems. Do you have a simple end elegant root finder that you would recommend? Thanks!
RE: Recommend root-finder for HP 67 - Namir - 11-30-2019 03:08 AM
Here is the code for Newton's method for the HP-67:
Code:
Memory Map
============
R0 = Torelance
R1 = x
R2 = h
R3 = fx(x)
Listing
=======
LBL A
STO 1 # Store x
RDN
STO 0 # Store tolerance
LBL 0 # start iteration loop
RCL 1
PAUSE # View curent guess for root
ABS
1
+
EEX
2
CHS
*
STO 2 # Store h
RCL 1
GSB E # calculate fx(x)
STO 3
RCL 1
RCL 2
+
GSB E # calculate fx(x+h)
RCL 3
-
1/X
RCL 3
*
RCL 2
* # Calculate difference
STO- 1 # X = X - difference
ABS
RCL 0
X<=Y? # |difference| >= tolerance?
GTO 0 # resume iteration
RCL 1 # display x
RTN
LBL E # define f(x)
EXP
LASTX
X^2
3
*
-
RTNLoad the above program. Edit the code in LBL E to implement the function you want to find the root for. Then:
1) Enter the tolerance value.
2) Press Enter.
3) Enter the guess for the root.
4) Press the A key.
5) The program will display the intermediate guesses for the solution using a PAUSE statement. Then the program displays the refined guess for the root, based on the tolerance value supplied.
You can calculate fx(x) values by entering a value for x and then pressing the E key.
RE: Recommend root-finder for HP 67 - Trond - 11-30-2019 04:44 AM
(11-30-2019 03:08 AM)Namir Wrote: Here is the code for Newton's method for the HP-67:
Code:
Memory Map
============
R0 = Torelance
R1 = x
R2 = h
R3 = fx(x)
Listing
=======
LBL A
STO 1 # Store x
RDN
STO 0 # Store tolerance
LBL 0 # start iteration loop
RCL 1
PAUSE # View curent guess for root
ABS
1
+
EEX
2
CHS
*
STO 2 # Store h
RCL 1
GSB E # calculate fx(x)
STO 3
RCL 1
RCL 2
+
GSB E # calculate fx(x+h)
RCL 3
-
1/X
RCL 3
*
RCL 2
* # Calculate difference
STO- 1 # X = X - difference
ABS
RCL 0
X<=Y? # |difference| >= tolerance?
GTO 0 # resume iteration
RCL 1 # display x
RTN
LBL E # define f(x)
EXP
LASTX
X^2
3
*
-
RTN
Load the above program. Edit the code in LBL E to implement the function you want to find the root for. Then:
1) Enter the tolerance value.
2) Press Enter.
3) Enter the guess for the root.
4) Press the A key.
5) The program will display the intermediate guesses for the solution using a PAUSE statement. Then the program displays the refined guess for the root, based on the tolerance value supplied.
You can calculate fx(x) values by entering a value for x and then pressing the E key.
Thanks! I am looking in vain for "RDN", do you mean "RND"?
EDIT: ah, I guess it's "roll down"
EDIT2: and "EXP" would be yX right?
EDIT3: What needs to remain in "E"? Should it always start with LASTX, and then put my function behind that?
RE: Recommend root-finder for HP 67 - Namir - 11-30-2019 06:14 AM
EXP is e^X.
LBL E ia the label you use to code f(x)=0. In my example, f(x)=e^x-3*x^2. You can start the code for f(x) by storing the value of x in an unused register, so you can reuse it to calculate x. I chose LASTX is recall X after calculate e^x.
Namir
RE: Recommend root-finder for HP 67 - Trond - 11-30-2019 05:17 PM
(11-30-2019 06:14 AM)Namir Wrote: EXP is e^X.
LBL E ia the label you use to code f(x)=0. In my example, f(x)=e^x-3*x^2. You can start the code for f(x) by storing the value of x in an unused register, so you can reuse it to calculate x. I chose LASTX is recall X after calculate e^x.
Namir
Ah that makes sense. Sorry, I was a bit tired yesterday. And it works! Thank you very much!