By Kiusalaas, J
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Example text
5) × Eq. (a) Eq. (c) ← Eq. 25 × Eq. 25 (c) This completes the first pass. Now we pick (b) as the pivot equation and eliminate x 2 from (c): Eq. (c) ← Eq. 5) × Eq. 5 3x 3 = 9 (a) (b) (c) The elimination phase is now complete. The original equations have been replaced by equivalent equations that can be easily solved by back substitution. As pointed out before, the augmented coefficient matrix is a more convenient instrument for performing the computations. 0 It is important to note that the elementary row operation in Eq.
5 Use Doolittle’s decomposition method to solve the equations Ax = b, where ⎡ ⎤ ⎡ ⎤ 1 4 1 7 ⎢ ⎥ ⎢ ⎥ A = ⎣1 b = ⎣ 13 ⎦ 6 −1 ⎦ 2 −1 2 5 Solution We first decompose A by Gauss elimination. 5 4 2 0 ⎤ 1 ⎥ −2 ⎦ −9 comes next. 5(6) = 18 50 Systems of Linear Algebraic Equations Finally, the equations Ux = y, or ⎡ 1 4 ⎢ U y = ⎣0 2 0 0 1 −2 −9 ⎤ 7 ⎥ 6⎦ 18 are solved by back substitution. 6 Compute Choleski’s decomposition of the matrix ⎡ ⎤ 4 −2 2 ⎢ ⎥ A = ⎣ −2 2 −4 ⎦ 2 −4 11 Solution First we note that A is symmetric.
8 Writing and Running Programs MATLAB has two windows available for typing program lines: the command window and the editor/debugger. The command window is always in the interactive mode, so that any statement entered into the window is immediately processed. The interactive mode is a good way to experiment with the language and try out programming ideas. MATLAB opens the editor window when a new M-file is created, or an existing file is opened. The editor window is used to type and save programs (called script files in MATLAB) and functions.