The Dynamics of Matrix Coupling with an Application to Krylov Methods
نویسنده
چکیده
Given the matrices A and E in Cn×n, we consider, for the family A(t) = A+ tE, t ∈ C, questions such as i) existence and analyticity of t 7→ R(t, z) = (A(t) − zI)) , and ii) limit as |t| → ∞ of σ(A(t)), the spectrum of A(t). The answer depends on the Jordan structure of 0 ∈ σ(E), more precisely on the existence of trivial Jordan blocks (of size 1). The results of the theory of Homotopic Deviation are then used to analyse the convergence of Krylov methods in finite precision.
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