کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4603432 1336960 2006 21 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Cluster robust error estimates for the Rayleigh–Ritz approximation I: Estimates for invariant subspaces
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Cluster robust error estimates for the Rayleigh–Ritz approximation I: Estimates for invariant subspaces
چکیده انگلیسی

This is the first part of a paper that deals with error estimates for the Rayleigh–Ritz approximations to the spectrum and invariant subspaces of a bounded Hermitian operator in a Hilbert or Euclidean space. This part addresses estimates for the angles between the invariant subspaces and their approximations via the corresponding best approximation errors and residuals and, for invariant subspaces corresponding to parts of the discrete spectrum, via eigenvalue errors. The paper’s major concern is to ensure that the estimates in question are accurate and ‘cluster robust’, i.e. are not adversely affected by the presence of clustered, i.e. closely situated eigenvalues in the spectrum. Available estimates of such kind are reviewed and new estimates are derived. The paper’s main new results introduce estimates for invariant subspaces in which the operator may have clustered eigenvalues whereby not only the distances between eigenvalues in the cluster are not present but also the distances between the cluster and the rest of the spectrum appear in asymptotically insignificant terms only.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 415, Issue 1, 1 May 2006, Pages 167-187