Unformatted text preview: by σ n ± x − x true ± . Therefore σ n ± x − x true ± ≤ ( ± b − b true + r ± ) , and the statement follows. For any matrix C and any vector z , ± Cz ± ≤ ± C ±± z ± . Therefore, ± b true ± = ± Ax true ± ≤ ± A ±± x true ± . (c) Using the given fact and the second statement, we see that ± x true ± ≥ 1 σ 1 ± b true ± . Dividing the ±rst statement by this one gives ± x − x true ± ± x true ± ≤ σ 1 σ n ± b − b true + r ± ± b true ± = κ ( A ) ± b − b true + r ± ± b true ± ....
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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.
 Fall '11
 Dr.Robin

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