Differential Equations Solutions 1

Differential Equations Solutions 1 - 11 Equations for...

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Unformatted text preview: 11 Equations for Linear System 1 Equations for Linear System 2 2 4 1.8 2 1.6 1.4 0 x2 x2 1.2 1 −2 0.8 −4 0.6 0.4 −6 0.2 0 −2 −1.8 −1.6 −1.4 −4 6 −1.2 −1 x1 −0.8 −0.6 −0.4 −0.2 −8 −5 0 −3 −2 −1 −4 Residuals for Linear System 1 x 10 −4 8 0 x1 1 2 3 4 5 Residuals for Linear System 2 x 10 6 4 4 2 r2 r2 2 0 0 −2 −2 −4 −4 −6 −6 −4 −2 −4 6 0 r1 2 4 −6 −6 6 −4 −2 Changes in x for Linear System 1 x 10 0 r1 −4 x 10 2 4 6 −4 x 10 Changes in x for Linear System 2 0.15 0.1 4 0.05 2 δ x2 δ x2 0 0 −0.05 −2 −0.1 −4 −0.15 −6 −10 −8 −6 −4 −2 δ x1 0 2 4 6 8 −4 x 10 −0.2 −0.2 −0.15 −0.1 −0.05 δ x1 0 0.05 0.1 Figure 2.1. Results of Challenge 2.2. The example on the left is typical of well-conditioned problems, while the example on the right is ill-conditioned, so the solution is quite sensitive to noise in the data. The graphs at top plot the linear equations, those in the middle plot residuals to perturbed systems, and those on the bottom plot the corresponding solution vectors. 0.15 ...
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This note was uploaded on 01/21/2012 for the course MAP 3302 taught by Professor Dr.robin during the Fall '11 term at University of Florida.

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