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HW5assignment

HW5assignment - HW#5 Due EGM6341 Fall 2009 From textbook by...

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HW#5 EGM6341 Fall 2009 Due: 2/26/09 From textbook by Atkinson pp185-194 #6 Suppose that you are to making a table of values of sin(x), 0 < x < π/2 with a stepsize of h. assume linear interpolation is to be used with the table, and suppose the total error, including the effects due to rounding in the table entries is to be at most . What should h equal (choose it in a convenient size for actual use) and to how many significant digits should the table entries be given? #11 Let be distinct real points, and consider the following interpolation problem. Choose a function such that with the {y i } given data. Show there is a unique choice of c 0 ,…c n . Hint: the problem can be reduced to that of ordinary polynomial interpolation. #18 Do an inverse interpolation problem using the table for J 0 (x) given in Section 3.2 x f 2 0.223890779 2.1 0.16660698 2.2 0.110362267 2.3 0.055539784 2.4 0.002507683 2.5 -0.048387764 2.6 -0.096804954 2.7 -0.14244937 2.8 -0.185036033

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2.9 -0.224311548 Find the value of x for which J 0 (x)=0, that is, calculate an accurate estimate of the root. Estimate your accuracy, and compare this with the actual value x=2.4048255577. #20 Consider the following table of values for
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