program4 - proportional to κ A k M Submission of Results...

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Program 4 Numerical Linear Algebra 1 Fall 2011 Due date: via email by 11:59PM on Wednesday, 11/16/11 General Task Defne the random matrix A R 50 × 10 via Udiag (1 , 10 - 1 , . . . , 10 - 9 ) V T where U R 50 × 50 and V R 10 × 10 are random orthogonal matrices. The singular values oF A are thereFore 1 , 10 - 1 , . . . , 10 - 9 and the condition number is κ ( A ) 2 10 9 . Let A k be the matrix consisting oF the frst k columns oF A and let κ ( A k ) 2 ,F be the condi- tion number oF A k using either the matrix 2-norm or the matrix ±robenius norm. Implement both Classical and Modifed Gram-Schmidt and assess their relative loss oF orthogonality over the various ranges oF columns by evaluating For each k κ ( A k ), b I k Q T k Q k b 2 , and b I k V T k V k b 2 , where Q k is computed via classical Gram-Schmidt and V k is computed by modifed Gram-Schmidt. OF course, you should examine these values For several samples oF U and V . Does the loss oF orthogonality For classical occur more rapidly and severely when compared to the modifed algorithm? Is the loss oF orthogonality For the modifed algorithm
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Unformatted text preview: proportional to κ ( A k ) ǫ M ? Submission of Results Expected results comprise: 1. A document describing important aspects oF the code, the tests used and the results generated to validate the correct Functioning oF the code. You should write this in a manner intended to convince me that your code behaves correctly. 2. The source code, makefles, and instructions on how to compile and execute your code including the machine used iF applicable. 3. Code documentation should be included in each routine. These results should be emailed to [email protected] by 11:59PM on the due date above. You may be asked to demonstrate your code iF your document does not completely convince me that you tested your code su²ciently. 1...
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