ESM3A HW4 - Jacobs University Bremen School of Engineering and Science Peter Oswald Fall Term 2010 120201 ESM3A — Problem Set 4 Issued 29.9.2010

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Unformatted text preview: 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...
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This note was uploaded on 02/06/2011 for the course ESM 3A taught by Professor Prof. dr. peter oswald during the Spring '11 term at Jacobs University Bremen.

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ESM3A HW4 - Jacobs University Bremen School of Engineering and Science Peter Oswald Fall Term 2010 120201 ESM3A — Problem Set 4 Issued 29.9.2010

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