Iterative Eigenvalue Estimation using Cholesky Decomposition

Iterative Eigenvalue Estimation using Cholesky Decomposition with Permutation

The proposed algorithm achieves a moderate convergence performance, comparable to the classical QR iterations (with permutations) [1], at a lower computational cost. It uses a combination of the low-complexity (N^3/6 per step) Cholesky iterations [2] together with matrix permutation based on the diagonal values. The algorithm works for positive definite matrices and can be extended to work on positive-semi definite, symmetric, and arbitrary matrices using methods described in [1] and [2].

References:
[1] Symmetric QR Algorithm with Permutations, arXiv:1402.5086.
[2] Singular Values using Cholesky Decomposition, arXiv:1202.1490.

Package: This package demonstrates the proposed algorithm.
Run instructions: Run test_choliter.m
Example output: test_choliter.fig or test_choliter.png