内容讲义文稿hw1 sol.pdfVIP

CS412, Fall 2013 Solutions for Assignment # 1 Prepared by Yimin Tan Sep 25, 2013 1 Problem # 1 (15 points) This is the output obtained after completing the file ck1.m: >> ck1 h(i) error 2.5000e-03 1.8482e-05 6.2500e-04 4.6222e-06 1.5625e-04 1.1557e-06 3.9063e-05 2.8892e-07 9.7656e-06 7.2224e-08 2.4414e-06 1.8063e-08 6.1035e-07 4.6936e-09 1.5259e-07 1.4194e-09 3.8147e-08 -3.5820e-11 9.5367e-09 1.1606e-08 2.3842e-09 -3.4960e-08 5.9605e-10 1.5130e-07 1.4901e-10 1.5130e-07 3.7253e-11 -1.3388e-06 (2 points) This program computes the derivative of atan(x) at x = 5 (so TRUEV = 1/(5 ∗ 5 + 1)). (3 points) The method used here is called forward difference quotient. The output with the new D is >> ck1 h(i) error 2.5000e-03 -8.7714e-09 6.2500e-04 -5.4830e-10 1.5625e-04 -3.4399e-11 3.9063e-05 -1.7140e-12 9.7656e-06 -1.7140e-12 2.4414e-06 9.6546e-12 6.1035e-07 1.4608e-10 1.5259e-07 -3.5820e-11 3.8147e-08 -3.5820e-11 9.5367e-09 -3.5820e-11 2.3842e-09 -3.4960e-08 5.9605e-10 -3.4960e-08 1.4901e-10 1.5130e-07 3.7253e-11 -1.3388e-06 This program is still computing the derivative of atan(x) at x = 5. (2 points) The method used this time is called symmetric difference quotient. There are two major conclusions that could be drawn: a) Both methods have a loss of significance when h is small enough, due to the subtra