  We present an efficient algorithm to compute the induced norms of
finite-horizon Linear Time-Varying (LTV) systems. The formulation includes both
induced $\mathcal{L}_2$ and terminal Euclidean norm penalties. Existing
computational approaches include the power iteration and bisection of a Riccati
Differential Equation (RDE). The power iteration has low computation time per
iteration but overall convergence can be slow. In contrast, the RDE condition
provides guaranteed bounds on the induced gain but single RDE integration can
be slow. The complementary features of these two algorithms are combined to
develop a new algorithm that is both fast and provides provable upper and lower
bounds on the induced norm within the desired tolerance. The algorithm also
provides a worst-case disturbance input that achieves the lower bound on the
norm. We also present a new proof which shows that the power iteration for this
problem converges monotonically. Finally, we show a controllability Gramian
based simpler computational method for induced $\mathcal{L}_2$-to-Euclidean
norm. This can be used to compute the reachable set at any time on the horizon.
Numerical examples are provided to demonstrate the proposed algorithm.
