A quadratically convergent parallel Jacobi process for diagonally dominant matrices with nondistinct eigenvalues

AbstractThis article presents a new Jacobi-like eigenvalue algorithm for non-Hermitian almost diagonal n×n matrices. In each step n2 submatrices of order 2 are diagonalized. The precautions for the multiple eigenvalues are based on theorems of Fan and Hoffman (1954) and Wilkinson (1961). The proof of the quadratic convergence generalizes our previous result for distinct eigenvalues. The convergence theorem is pessimistic concerning the region of attraction to a diagonal. The local information structure makes the process suitable for parallelization on a hypercube or a systolic array