Answer Happy

Recall that K2(A) = 120.94. Colin solves this problem using the method of normal equations. Assume that the data values y; have been measured to 9 significant figures, and assume that the values of x; are known exactly. Estimate the relative error in Colin's solution u. Incorrect relative error in uŹ 1.2094*10^-7 ant figures. Your Answer: 1.2094*10^-7 Correct Answer: 7.313243E-6 + 5.0%
Riley, Orion and Colin challenge you to find the quadratic polynomial of best fit in the least squares sense for the data points below: 1 2 4 5 6 j 20j 1 1.2 3 1.4 1.6 1.6 1.8 2 0.5 Yj 2 1.4 1 1.2 Orion reminds you to formulate this problem as a linear system Au = y, with y being a column vector of the data values y; and with A being an m-by-n matrix depending on the values r;. Colin says you can then use appropriate commands in MATLAB to solve this problem Riley tells you that the matrix A has condition number K2(A) 120.94. Use this information as a consistency check to be sure that you have defined A correctly in MATLAB. (a) [1 mark] Orion wonders whether you have a matrix of the right size. What are the values of m and n? m = 6 and n = 3 (b) [2 marks] Give the approximation you obtained. y(x) = 2.67-0.573*X-0.223*x^2 Give your coefficients to at least 3 significant figures. Remember to type the multiplication symbol whenever appropriate. Click on the preview button to double check your answer. (c) (1 mark] Use your approximation to estimate the data value at x = 1.256 y(1.256) 1.599 Give your answer to at least 3 significant figures. (d) [1 mark] Recall that K2(A) 120.94. Colin solves this problem using the method of normal equations. Assume that the data values y; have been measured to 9 significant figures, and assume that the values of x, are known exactly. Estimate the relative error in Colin's solution u relative error in u 1.2094*10^-7 Give your answer to at least 2 significant figures. (e) [2 marks] Following on from part (d), do you have confidence in Colin's solution? Suppose instead Riley solves this problem using the method of QR factorization. How might the relative error in u change? Explain your answers by referring explicitly to Colin's and Riley's solutions.