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Unformatted text preview: IE170 Lab #12 Prof. Linderoth IE 170 Lab #12: Least Squares Due: May 4, 2007 1 Description and Objectives In this (our final) lab, you will put together many of the matrix operations that you have learned to produce an application that can solve Least Squares problems from scratch. This is a farily involved lab. (Sorry.) But on the bright side, you will have a good while to finish it. Lab Objectives 1. Understand DenseMatrix class operations from previous lab. 2. Implement a Cholesky Factorization routine for solving (dense) symmetric positive def- inite linear systems 3. Understand how to use the Cholesky Factorization to solve a linear system 4. Learn how to create the normal equations that are required for a least squares curve fitting, including operations for matrix transpose 5. Solve the linear system(s) necessary to perform a least-squares curve fitting 2 Cholesky Decomposition Our first step towards our goal of having a least squares solver is to build a class that can factorize a symmetric positive definite matrix into lower and upper triangular parts:...
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- Spring '07
- Systems Engineering