SIAM Journal on Matrix Analysis and Applications
The symmetric eigenvalue problem
The symmetric eigenvalue problem
Understanding Klylov Methods in Finite Precision
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
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Given the matrices A and E in Cn×n, we consider, for the family A(t)=A+t(E), t∈C, questions such as i) existence and analyticity of t ↦R(t,z)=(A(t)−zI)−1 , 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.