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Algorithm behind NSolve

Kashif Nazar, UTM,Malaysia
Posted 10 years ago

Hello,

Can anyone guide me that which algorithm or Method is behind Mathematica Command " NSolve"

Thanks
POSTED BY: Kashif Nazar
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There are different methods based on type of input (single equation, linear system, polynomial system, domain specification, etc.).
POSTED BY: Daniel Lichtblau

It might be using a sparse homotopy method (in version 10). Or a method based on numeric Groebner bases and eigensystem computation. Depending on the specifics either one could be slow.
POSTED BY: Daniel Lichtblau

All methods based on Groebner bases are exponential in complexity. Polyhedral homotopy might be better in theory and is often better in practice, in terms of speed at least. Though there is an initialization step that is not cheap.

I do not know of any solver in Mathematica which would be faster than NSolve and not require an initial guess. Maybe try FindMinimum or NMinimize on the sum of squares is about all that comes to mind.
POSTED BY: Daniel Lichtblau

Thanks Sir,

its being a long time i am facing problem in using Mathematica Command "NSolve". The Problem is that i have a system of 10 non-linear equations with 10 variables.

Upto a system of 8 equations i am getting my results, but for a system of 10 non-linear equations with 10 variables, i kept running my program but dont get my results even after many many hours long time. So i just wanted to know which method or algorithm is behind "NSolve" so that i may figure out anything.

Thanks
POSTED BY: Kashif Nazar

Thanks once again,

Can you please suggest any other similar command in mathematica which dont require any initial guess.
POSTED BY: Kashif Nazar

Are these methods polynomial or exponential in complexity?
POSTED BY: Frank Kampas
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