Differential Equations Solutions 163

Differential Equations Solutions 163 - x ( k +1) = x ( k )...

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Chapter 28 Solutions: Iterative Methods for Linear Systems CHALLENGE 28.1. See Solution to Challenge 6. CHALLENGE 28.2. See the answer to Challenge 6. CHALLENGE 28.3. See the answer to Challenge 6. CHALLENGE 28.4. Consider our stationary iterative method Mx ( k +1) = Nx ( k ) + b or x ( k +1) = M 1 Nx ( k ) + M 1 b . Manipulating these equations a bit, we get
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Unformatted text preview: x ( k +1) = x ( k ) + ( M 1 N I ) x ( k ) + M 1 b = x ( k ) + M 1 ( N M ) x ( k ) + M 1 b = x ( k ) + M 1 ( b Ax ( k ) ) = x ( k ) + M 1 r ( k ) . CHALLENGE 28.5. See the answer to Challenge 6. 173...
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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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