On weakly formulated Sylvester equations and applications (CROSBI ID 118616)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Grubišić, Luka ; Veselić, Krešimir
engleski
On weakly formulated Sylvester equations and applications
We use a ``weakly formulated'' Sylvester equation $$A^{; ; ; ; 1/2}; ; ; ; TM^{; ; ; ; -1/2}; ; ; ; -A^{; ; ; ; -1/2}; ; ; ; TM^{; ; ; ; 1/2}; ; ; ; =F$$ to obtain new bounds for the rotation of spectral subspaces of a nonnegative selfadjoint operator in a Hilbert space. Our bound extends the known results of Davis and Kahan. Another application is a bound for the square root of a positive selfadjoint operator which extends the known rule: ``The relative error in the square root is bounded by the one half of the relative error in the radicand''. Both bounds are illustrated on differential operators which are defined via quadratic forms.
eigenvalues ; eigenvectors ; variational methods for eigenvalues of operators ; perturbation theory
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Podaci o izdanju
58 (2)
2007.
175-204
objavljeno
0378-620X
1420-8989
10.1007/s00020-007-1482-4