Implicit QR for rank-structured matrix pencils
A fast implicit QR algorithm for eigenvalue computation of low rank corrections of Hermitian matrices is adjusted to work with matrix pencils arising from zerofinding problems for polynomials expressed in Chebyshev-like bases. The modified QZ algorithm computes the generalized eigenvalues of certain \(N\times N\) rank structured matrix pencils using \(O(N^2)\) flops and \(O(N)\) memory storage. Numerical experiments and comparisons confirm the effectiveness and the stability of the proposed method.
rank-structured matrix eigenvalue computation qz algorithm quasiseparable matrix chebyshev approximation complexity 65f15 65h17