Dissertation/ Thesis
Superoptimal analytic approximation and exterior products
| العنوان: | Superoptimal analytic approximation and exterior products |
|---|---|
| المؤلفون: | Chiotis, Dimitrios |
| بيانات النشر: | University of Newcastle upon Tyne, 2020. |
| سنة النشر: | 2020 |
| المجموعة: | University of Newcastle Upon Tyne University of Newcastle upon Tyne |
| مصطلحات موضوعية: | 515 |
| الوصف: | This dissertation concerns the classical problem of finding a bounded analytic function on the unit disc D which approximates a given essentially bounded function G on the unit circle T as well as possible in the L1 norm. In the case that G is a continuous mxn matrix-valued function on T; there is a typically large set of optimal bounded analytic approximants in the L1 norm, and it is therefore natural to study bounded analytic approximants Q on D for which G - Q is minimised in a strengthened sense. One de nes, for j 0; s1 j (G Q) = ess sup z2T sj(G(z) Q(z)); where s0; s1; : : : ; sj are the singular values of a matrix. One then says that a bounded analytic matrix function Q is a superoptimal analytic approximant of G if Q lexicographically minimises the sequence (s1 0 (G Q); s1 1 (G Q); : : : ; ) over all bounded analytic matrix functions. It is known that every continuous matrix-valued function on T has a unique superoptimal analytic approximant AG; moreover, for rational G; there are numerical procedures for the calculation of AG: Existing algorithms are computationally intensive. This thesis introduces a new operator-theoretic technique, based on exterior powers of Hilbert spaces and operators, for the calculation of the superoptimal analytic approximants. The result is a new algorithm which avoids some of the lengthier and potentially more illconditioned steps in previously described algorithms. In particular, the present algorithm does not require the spectral factorisation of matrix-valued positive functions on T. |
| نوع الوثيقة: | Electronic Thesis or Dissertation |
| اللغة: | English |
| URL الوصول: | https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.833114 |
| رقم الانضمام: | edsble.833114 |
| قاعدة البيانات: | British Library EThOS |
| الوصف غير متاح. |