Homework 7 Bob 28.1

Homework 7 Bob 28.1 - 28.1) T he results and information...

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28.1) The results and information for Problem 28.1 appear in the following order: evaluation of the binomial without expansion; the evaluation of the polynomial generated from expanding the binomial; the graph of the outputs; numerical outputs; error findings; and, finally, error analysis. >> f1 = inline('(x-2).^9','x') f1 = Inline function:5 f1(x) = (x-2).^9 >> x=1.92:.001:2.08; >> y1=f1(x); >> plot(x,y1,'blue') >> f2 = inline('x.^9 - 18.*x.^8 + 144.*x.^7 - 672.*x.^6 + 2016.*x.^5 - 4032.*x.^4 + 5376.*x.^3 - 4608.*x.^2 + 2304.*x - 512','x') f2 = Inline function: f2(x) = x.^9 - 18.*x.^8 + 144.*x.^7 - 672.*x.^6 + 2016.*x.^5 - 4032.*x.^4 + 5376.*x.^3 - 4608.*x.^2 + 2304.*x - 512 >> y2=f2(x); >> hold on >> plot(x,y2,'red') In theory the graphs should be the same however in practice errors arise as the topic of the chapter implies. A comparison of the output for y1 and y2 can be found in the lists on the following pages. Y1 is in the left column and y2 is in the right. An examination of the graphs and two columns of data will indicate that y1 follows a smooth progression while y2 has fluctuations both positive and negative in respect to y1. Both methods of the calculation return 0 for f(2)
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>> f1(2) ans = 0 >> f2(2) ans = 0 Output of the two methods of calculations >> y1 y1 = 1.0e-009 * Columns 1 through 7 -0.1342 -0.1199 -0.1069 -0.0952 -0.0846 -0.0751 -0.0665 Columns 8 through 14 -0.0589 -0.0520 -0.0458 -0.0404 -0.0355 -0.0311 -0.0272 Columns 15 through 21 -0.0238 -0.0207 -0.0180 -0.0156 -0.0135 -0.0117
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This note was uploaded on 01/15/2011 for the course MATH 345 taught by Professor Staff during the Spring '08 term at Ohio State.

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Homework 7 Bob 28.1 - 28.1) T he results and information...

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