Computing the -induced norm of a compression operator via fast-lifting

This paper studies computing the induced norm of a compression operator defined on the Banach space L ∞ [ 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 [ 0 , 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.