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# HW11-1 - dominant eigenvalue You may use a calculator for...

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EMAE 250: Homework 11 April 15, 2011 1. For the following matrix: A = 2 4 - 1 3 0 2 1 1 0 (a) [1pt] Using Matlab, find Q and R by using the following commend: ‘[Q, R] = qr(A)’. (b) [2pt] For Q and R , perform three iterations of the QR algorithm for finding eigenvalues of A . You may use a calculator for numerical computations, but show computational steps by hand. (c) [1pt] Compute the eigenvalues of A by using the formula det( A - λ I ) = 0 and compare the result with (b). What is the true percentage relative error in the
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Unformatted text preview: dominant eigenvalue? You may use a calculator for numerical computations, but show computational steps by hand. 2. A steady-state heat balance for a rod can be represented as d 2 T dx 2-. 15 T = 0 . (a) [3pt] For given T(0) = 40 and T(4) = 100, use the shooting method to ﬁnd T(2). (b) [3pt] Use the ﬁnite-diﬀerence approach with Δ x = 1 to solve the above problem. 1...
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