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# hw11 - x 9/f 9-x 11/f 11 This code will run many many times...

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MAE 107 Assignment 1 Due Thursday, 30 Sept., 2010 Problems to hand in (Not all problems may be graded.) 1. Epperson, Section 1.1 problems: 2, 5, 9, 10a, 11a, 11b, 12c, 15. Note: Use formula (1.3) for the error estimates in problems 11a and b. 2. Epperson, Section 1.2 problems: 1, 3, 10. 3. Epperson, Section 1.3 problems: 1b, 2b, 3b, 7. 4. You need to compute sin( x ) for x [0 , π ] on a low-level processor/compiler. Only the operations + , - , × , ÷ are available. You’ve been told that it only has “roughly 4 digits” of accuracy. Your coworker has written the following pseudo-code (essentially MATLAB). input x; x 3 = x * x * x ; x 5 = x 3 * x * x ; x 7 = x 5 * x * x ; x 9 = x 7 * x * x ; x 11 = x 9 * x * x ; f 3 = 6; f 5 = 5 * 4 * f 3; f 7 = 7 * 6 * f 5; f 9 = 9 * 8 * f 7; f 11 = 11 * 10 * f 9; sinx = x - x 3 /f 3 + x 5 /f 5 - x 7 /f

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Unformatted text preview: x 9 /f 9-x 11 /f 11; This code will run many, many times, and so needs to be fast. Using what you know about Taylor series, can you improve on your coworker’s code? (Do not go so far as table look ups and/or if/then logic.) Indicate what you would do. All the above problems (if graded) are worth 5 points, except the ﬁnal problem which is worth 10 points. 1 Study Problems (Will not be graded.) • Epperson, Section 1.1 problems: 1, 4, 10b, 11d, 12b, 12d, 14, 25. Note: Use formula (1.3) for the error estimates in problem 11d. • Epperson, Section 1.2 problems: 6, 14. • Epperson, Section 1.3 problems: 1a, 2a, 2c. 2...
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hw11 - x 9/f 9-x 11/f 11 This code will run many many times...

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