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

This paper is concerned with the computation of the induced norm of a compression operator defined on the Banach space L
∞
[0, h), which is a difficult problem because it is an infinite-rank operator. This paper provides two methods 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. Another key idea in both methods is to apply fast-lifting by which the interval [0, h) is divided into M subintervals with equal width, and the computation errors in these methods are ensured to be reciprocally proportional to M or M
²
. The effectiveness of the proposed methods is demonstrated through a numerical example.