Consider an iterative algorithm generating a sequence {x'}t>1 in R" that converges to x* E R". We seek to characterize the rate of convergence via two values p e N and 0 < B < o∞ by finding the largest p such that - x lim sup く0. t→" ||æt-1 - x* ||P Let 0 < 8 < 1 and define a sequence rį = ||x* – x* ||. Categorize the convergence of the following sequences as sublinear, linear, superlinear, or quadratic. Justify and explain your answers. (a) rt = (b) rị = 8t (c) Tt = St2

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