Replace KPM with Lanczos

[kbarros]

The Lanczos algorithm promises these benefits relative to KPM:

• Higher accuracy at a fixed number of iterations (i.e., at a fixed Krylov subspace dimension).
• Allows for a sharp cutoff between positive and negative eigenvalues near zero. Whereas KPM is susceptible to a loss of intensity near Goldstone modes, Lanczos seems to avoid this problem.
• Does not require an initialization phase that bounds the spectrum prior to polynomial expansion.
• Ability to detect instabilities (negative eigenvalues) in the dynamical matrix.

As currently implemented, Lanczos is currently slower than KPM per iteration. But because many fewer iterations are required, Lanczos still seems favorable in overall speed. And future optimizations may be possible, e.g., operating on multiple right-hand side vectors in parallel.

Possible disadvantages of Lanczos may become apparent when the number of iterations becomes large (e.g., in the hundreds and beyond). Numerical roundoff error may accumulate -- the empirical effects of this will require testing. Also, Lanczos requires direct diagonalization of a tridiagonal matrix, and this cost may eventually dominate after a very large number of iterations.

See https://arxiv.org/abs/2410.11090 for a modern mathematical review of the Lanczos method, including a numerical stability analysis in Sec. 4.