How calculate programs/packages like Matlab, Python/scipy, ...the inverse jacobian for multidimensional Newton's method? x_(n+1)=xn−(J(x_n)^(−1)∗f(x_n))

Vorbeckenuc 2022-07-18 Answered
How calculate programs/packages like Matlab, Python/scipy, ...the inverse jacobian for multidimensional Newton's method?
x n + 1 = x n ( J ( x n ) 1 f ( x n )
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Vartavk
Answered 2022-07-19 Author has 11 answers
Most numerical packages give you the option of either computing the Jacobian yourself and passing it to the solver, or of numerically approximating it with a finite difference scheme. I imagine that in general while performing Newton's method or other methods expressed in terms of an inverse Jacobian, these packages do not actually compute the inverse for reasons of stability. Instead, they solve the linear system J ( x n ) x n + 1 = J ( x n ) x n f ( x n ) for x n + 1 at each time step.
The Jacobian is not always invertible; in order to use Newton's method the Jacobian must be invertible, though. You can see this in one dimension, with a function R R with a critical point which is not an extremum.
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

New questions