• continuous spectra and numerical eigenvalues

    نویسندگان :
    جزئیات بیشتر مقاله
    • تاریخ ارائه: 1392/07/24
    • تاریخ انتشار در تی پی بین: 1392/07/24
    • تعداد بازدید: 935
    • تعداد پرسش و پاسخ ها: 0
    • شماره تماس دبیرخانه رویداد: -
     some spectral problems for differential operators are naturally posed on the whole real line, often leading to eigenvalues plus continuous spectrum. then the numerical approximation typically involves three processes: (a) reduction to a finite interval; (b) discretization; (c) application of a numerical eigenvalue solver such as the qr-algorithm.

    reduction to a finite interval and discretization typically eliminate the continuous spectrum. however, through round-off error, the continuous spectrum may show up again when the eigenvalue solver is applied. (in some sense, three wrongs make a right.) interestingly, not all parts of the continuous spectrum show up in the same way, however. we illustrate this observation by numerical examples. a perturbation argument, though non-rigorous, explains the observation.

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