Computational Methods: Homework Assignment for Chapter 5 - Prof. E. Cliff, Assignments of Aerospace Engineering

Download Computational Methods: Homework Assignment for Chapter 5 - Prof. E. Cliff and more Assignments Aerospace Engineering in PDF only on Docsity! AOE/ESM 2074 Introduction to Computational Methods due 12 October 2000 1. Read the remainder of Chapter 5 in the Chapman text. 2. Complete the Matlab function l solve.m by providing the backward substitution part of the code. 3. Write a Matlab code segment that will identify rows for the interchange step in the Gaussian elimination. More specifically, suppose at some point we have processed through row kk − 1 so that the diagonal element aa(kk − 1, kk − 1) is unity and the elements in the kk− 1 column below it are all zero. Prior to processing row k we want to consider a row interchange. For this purpose we want to identify the row from kk to the end that has the largest element (absolute value) in the current column kk. You are to provide the code that returns this row index. 4. You are given an array x (n x 1 ) of independent variables and a corresponding array y of dependent variables. We expect that there is a linear relation yı = mxı + b that approximates this data. You are to determine a least squares estimate for m and b. Specifically, consider the problem of finding m and b to minimize the fit error E(m, b) = n∑ ı=1 (yı −mxı + b)2 Analyze this problem and describe a way to calculate m and b given the data. Write a Matlab function that will accept arrays x and y as input and compute the corresponding m and b values. 1