Computing the L∞[0,h) -induced norm of a compression operator via fast-lifting

Abstract

This paper studies computing the induced norm of a compression operator defined on the Banach space L-infinity[0, h), which is a difficult problem since it is an infinite-rank operator. Two methods are provided for this problem, each of which can compute an upper bound and a lower bound of the induced norm by using an idea of staircase or piecewise linear approximation. Staircase approximation and piecewise linear approximation are applied through fast-lifting, by which the interval 10, h) is divided into M subintervals with equal width, and the approximation errors in these methods are ensured to be reciprocally proportional to M or M-2. The effectiveness of the proposed methods is demonstrated through numerical examples. (C) 2014 Elsevier B.V. All rights reserved.