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Does anybody know what algorithm is used in the Hp50g Multiple Equation Solver?

The HP Solve Equation Library Application Card Owner's Manual says on page 169:

"When you solve problems using the Multiple-Equation Solver, the application uses the same numeric root finder that's used by the HP Solve application, which is built into the HP 48."

I assume that the same is true for the HP 50g.

(07-10-2020 03:27 AM)Joe Horn Wrote: [ -> ]The HP Solve Equation Library Application Card Owner's Manual says on page 169:

"When you solve problems using the Multiple-Equation Solver, the application uses the same numeric root finder that's used by the HP Solve application, which is built into the HP 48."

I assume that the same is true for the HP 50g.

Thanks Joe. Would that then be a non linear equation solver? Like Levenberg-Marquardt method?

(07-10-2020 10:44 AM)Tugdual Wrote: [ -> ]Would that then be a non linear equation solver? Like Levenberg-Marquardt method?

Anybody know? If it's the same as the solver that HP first introduced in the HP-34C, then it's a "modified secant iteration method" as explained here by Dr Kahan himself in 1979: https://people.eecs.berkeley.edu/~wkahan...LVEkey.pdf

(07-10-2020 12:13 PM)Joe Horn Wrote: [ -> ]

(07-10-2020 10:44 AM)Tugdual Wrote: [ -> ]Would that then be a non linear equation solver? Like Levenberg-Marquardt method?

Anybody know? If it's the same as the solver that HP first introduced in the HP-34C, then it's a "modified secant iteration method" as explained here by Dr Kahan himself in 1979: https://people.eecs.berkeley.edu/~wkahan...LVEkey.pdf

Thanks for the reading, Joe!

Not sure if this is what is used in the 50g but here is an HP patent for a multiple equation solver. It seems to be more about the multiple equation part than the solving of each equation.
https://patents.google.com/patent/US5175700
Method and apparatus for solving multiple equations

It also references this patent:
https://patents.google.com/patent/US4845652A/en
Generic equation solver interface for solving mathematical equations

Very much wish the Prime will eventually incorporate this type of multiple equation solving.

It sounds like this older topic might be relevant... not my area of expertise but hoping it may be useful: Multiple equation solver for the HP-28C (program)

Thanks all for the replies.
So to summarize it would be a sort of combination of an algo to try to solve obvious solutions, when only one variable remains and/or a secant method applied to multiple variables, hence something resembling https://en.wikipedia.org/wiki/Broyden%27s_method to expand on mutliple variables.