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Unformatted text preview: HOMEWORK II The exponent of a real number x can be deﬁned by the power series
∞s 1 1 x exp(x) = 1 + x + x2 + x3 + · · · = ∑ , 2 6 s=0 s! or by the limit exp(x) = lim 1 +
n→∞ x n n . In the same way, the exponent of a square symmetric matrix X can be deﬁned by the matrix power series
∞ 1 1 1 exp(X ) = I + X + X 2 + X 3 + · · · = ∑ X s , 2 6 s! s=0 or by the matrix limit Xn exp(X ) = lim I + . n→∞ n For your homework (1) Write R functions for both methods of approximating the exponential of a square symmetric matrix. Use a repeat loop, eps, itel, and verbose similar to what is done in iterator.R in the code directory. (2) Try it out on a diagonal matrix to see if your program is working correctly. (3) Describe what happens if you apply your functions to the asymmetric matrix X= 0 0 1 0 . Date: October 26, 2010 — 19h 44min — Typeset in T IMES ROMAN.
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This note was uploaded on 01/14/2011 for the course STATS 102A 102A taught by Professor Jandeleeuw during the Fall '10 term at UCLA.
- Fall '10