0-13 - CHAP 0 Mathematical Preliminaries 15 13 Consider the...

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CHAP 0 Mathematical Preliminaries 15 13. Consider the matrix equation [ A ]{ x } = { b } given by 1 2 3 2 1 0 4 1 2 1 0 0 1 2 4 x x x                            (a) Construct the quadratic form F" ( x ) = { x } T [ A ]{ x } 2{ x } T { b }. (b) Find { x } = { x * } by minimizing F ( x ). (c) Verify that the vector { x * } satisfies [ A ]{ x } = { b }. Solution: (a) The quadratic form F" ( x )=2F(x) is: 222 1 2 3 1 2 2 3 1 3 44 F x x x x x x x x x (b) Find { x } = { x * } that minimizes F ( x ). 12 1 0 2 4 F xx x 1 2 3 2 02 F x x x x   23 3 0 2 4 F x   By solving the above three equations with respect to three unknown, we can obtain: x 1 = 4, x 2 = 4, and
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This note was uploaded on 08/22/2011 for the course EML 4500 taught by Professor Staff during the Fall '08 term at University of Florida.

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