Computing the L∞[0,h)L∞[0,h)-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)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)[0,h) is divided into MM subintervals with equal width, and the approximation errors in these methods are ensured to be reciprocally proportional to MM or M2M2. The effectiveness of the proposed methods is demonstrated through numerical examples.