1

I would like to find the zeros of a real function of multiple variables. Many algorithms are known to solve this problem (such as the Newton-Rhapson method), but in the general case, do these problems belong to the NP-complete class of problems ? In other words do we know a method to solve this in reasonable time if the number of variables becomes high ?

Thanks in advance !

PS: I haven't found this question asked on the forum but some topics seem closely related, if my question is redundant please tell me.

C-Lvd
  • 11
  • 1
  • 2

1 Answers1

0

What is your input definition? Remember, for questions of complexity, you need to compare run times to the encoding length of the input.

And what do you understand as a "solution" in computer terms? One finite definition would be a box with rational corners containing exactly one solution. Or a similar box inside the domain of quadratic convergence of Newtons method. See the standard book of Blum/Shucker/Smale/?? on the complexity of the real numbers.

Even for polynomial problems the situation is complicated, it is not known if the solution of polynomial systems is in P or in NP.

Lutz Lehmann
  • 25,219
  • 2
  • 22
  • 51