The Faber–Manteuffel Theorem for Linear Operators
نویسندگان
چکیده
منابع مشابه
The Faber-Manteuffel Theorem for Linear Operators
A short recurrence for orthogonalizing Krylov subspace bases for a matrix A exists if and only if the adjoint of A is a low degree polynomial in A (i.e. A is normal of low degree). In the area of iterative methods, this result is known as the Faber-Manteuffel Theorem (V. Faber and T. Manteuffel, SIAM J. Numer. Anal., 21 (1984), pp. 352–362). Motivated by the description in (J. Liesen and Z. Str...
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Let V be a finite-dimensional vector space, either real or complex, and equipped with an inner product 〈· , ·〉. Let A : V → V be a linear operator. Recall that the adjoint of A is the linear operator A : V → V characterized by 〈Av, w〉 = 〈v, Aw〉 ∀v, w ∈ V (0.1) A is called self-adjoint (or Hermitian) when A = A. Spectral Theorem. If A is self-adjoint then there is an orthonormal basis (o.n.b.) o...
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ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2008
ISSN: 0036-1429,1095-7170
DOI: 10.1137/060678087