Behavior of a functional in learning theory
type: Item
instance of: scholarly article
title: Behavior of a functional in learning theory
zbMATH Open document ID: 1161.46012
author: Hongwei Sun
published in: Frontiers of Mathematics in China
publication date: 2008-07-29T00:00:00Z
review text: Let \(A:H\to H\) be a continuous linear operator on a Hilbert space \(H\), \(R(A)\) the range of \(A\), and let \(y\in H\) satisfy \(y\in\overline{R(A)}\) and \(y\notin R(A)\). The author studies the functional \(F(\tau)\) defined as \(\inf\{\|y-Ax\|^2:x\in H,\|x\|\leq\tau\}\), \(\tau\geq 0\). Assuming that \(y\in R((AA^*)^{t/2})\) for some \(0<t<1\) he proves that \(F(\tau)\leq\tau^{-\frac{2t}{1-t}}\|(AA^*)^{-\frac 12}y\|^{\frac{2}{1-t}}\), \(\forall\tau>0\).
reviewed by: Ludvík Janoš
Mathematics Subject Classification ID: 46C99
Mathematics Subject Classification ID: 68Q05
zbMATH DE Number: 5305334
MaRDI profile type: Publication
full work available at URL: s11464-007-0028-z
OpenAlex ID: W1866459861
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DOI: 10.1007/S11464-007-0028-Z
description: scientific article; zbMATH DE number 5305334