Parameter Identification Homework: Least Squares & Quadratic Models for Price Data - Prof., Assignments of Mathematics

Download Parameter Identification Homework: Least Squares & Quadratic Models for Price Data - Prof. and more Assignments Mathematics in PDF only on Docsity! Parameter Identification Homework 2 1. Consider the price data >> [time' price'] 1 2000 2 1960 3 1930 4 1905 5 1890 (a). Find matrix form of the least squares and the linear model mt + c. (b). Find and solve using Matlab the normal equations for m and c. (c). Use these m and c to predict the price a time equal to 10. 2. Consider the above price data, but now use the quadratic model. (a). Find matrix form of the least squares and the quadratic model at2 + bt + c. (b). Find and solve using Matlab the normal equations for a, b and c. (c). Use these to predict the price a time equal to 10. 3. As in lecture 6 on “Radioactive Parameter Identification” use the Matlab command fminsearch() to approximate the parameters u(0) and d so that the function for the amount at time t u(t) = u(0)e-dt is close to the following data, that is, the least squares function is a minimum. >> [time' amount'] 1 100 2 91 3 83 4 76 5 71