Roche concentrates on the stability of the finite sections method and the asymptotic behavior of singular values in his review of recent advancees and new results in the numerical analysis of the finite sections method for general band and band-dominated operators. His monograph, which can also serve as an introduction to this field of numerical analysis, works through stability, stable regularizability, including Moore-Penrose invertibility, compactness, including compact sequences and central rank characterizations, ...
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Roche concentrates on the stability of the finite sections method and the asymptotic behavior of singular values in his review of recent advancees and new results in the numerical analysis of the finite sections method for general band and band-dominated operators. His monograph, which can also serve as an introduction to this field of numerical analysis, works through stability, stable regularizability, including Moore-Penrose invertibility, compactness, including compact sequences and central rank characterizations, Fredholm properties, including sequences and stability, essential fractality, including singular values and finite sections algebras, and applications, including approximation numbers, rank-preserving disretizations, the Arevson dichotomy (in band-dominated operators and the general setting), essential spectra, essential pseudospectra, pseudomodes and determinants.
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