I have proposed an optimisation algorithm which I claim has improved upon the previous algorithm in a number of ways.
One of these claims is that my proposed solution requires no explicit SVD and psuedoinverse calculation which I claim is good, since in my case perturbations are important, and I believe these routines are traditionally unstable to perturbations.
My question is given the implementations in modern linear algebra computational libraries (such as LAPACK v3.0), how strong is this claim?
To summarise:
My method per iteration:
- Only one solution of a generalized eigenvalue problem
Old method per iteration:
- One solution of a generalized eigenvalue problem, AND,
- One explicit SVD calculation for a Jacobian, $J = USV^{\intercal}$
- Two explicit calculations of a pseudoinverse based on the Jacobian, $J$. That is, (1) $J^{\dagger}$ and (2) $V^{\dagger}$
Given that my algorithm will have input perturbations, and considering the stability of modern linear algebra routines, is my claim a strong selling point?