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# ESM3A HW4 - Jacobs University Bremen School of Engineering...

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Jacobs University Bremen School of Engineering and Science Peter Oswald Fall Term 2010 120201 ESM3A — Problem Set 4 Issued: 29.9.2010 Due: Wednesday 6.10.2010 (in class) This homework deals with applications of QR factorization (pseudo-inverse, least-squares solu- tion/approximation), and warms you up to the SVD. Consult the textbook by G. Strang [S] (or any other text on the subject of matrix calculations and linear algebra) and the script [MK] by K. Mallahi-Karai. 4.1. Let A = 1 1 2 1 1 2 , b = 2 5 / 2 7 / 2 . Find the least-squares solution of the linear system Ax=b. 4.2. a) Given m >> 3 measurement points ( t i , y i ), i = 1 , . . . , m , and three functions f ( t ), g ( t ), h ( t ). Suppose, you are told to find the parameters a , b , c such that y i af ( t i ) + bg ( t i ) + ch ( t i ) , i = 1 , . . . , m, is satisfied in a least-squares sense. Write down the corresponding normal equations (i.e., find formulas for the corresponding matrix A T A and right hand side A T b ). b) Data fitting can be reduced to the least-squares problem even in some cases, where it is not so obvious. Suppose your data satisfy

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• Spring '11
• Prof. Dr. Peter Oswald
• Singular value decomposition, Linear least squares, QR factorization, Peter Oswald, Jacobs University Bremen School of Engineering, maximum rank factorization

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