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The Rayleigh-Ritz method is widely used for eigenvalue approximation. Given a matrix X with columns that form an orthonormal basis for a subspace X , and a Hermitian matrix A, the eigenvalues of X H AX are called Ritz values of A with respect to X. If the subspace X is A-invariant then the Ritz values are some of the eigenvalues of A. If the A-invariant(More)
If x, y ∈ C n are unit-length vectors (x H x = y H y = 1) where y is an approximation to an eigenvector x of A = A H ∈ C n×n with Ax = xλ, λ = x H Ax ∈ R, then it is well known that the Rayleigh quotient y H Ay satisfies |λ − y H Ay| ≤ sin 2 θ(x, y).spread(A). (1) Here if λ 1 (A) ≥ · · · ≥ λ n (A) are the eigenvalues of A in descending order then spread(A)(More)
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