HW_Assignment_2 - computer to the next) 4.7 True value: f...

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HOMEWORK ASSIGNMENT 2 EGM 3344 Numerical Error Concepts Problems from Chapra book chapter 4 For all of these problems, feel free to use a simple Matlab program to calculate function values (like using a calculator) when the indicated approach is by hand. Problem Approach Comments 4.1 Hand Hint: First number is an integer, second number is a floating point. Write out solution equation by hand. Do calculations in Matlab if desired. 4.3 Matlab Call your Matlab program macheps.m 4.4 Matlab Skip the challenge question. 4.7 Hand Only do 3-digit arithmetic part. Write out all equations by hand and use Matlab or calculator for intermediate results. Chopping means truncate to only 3 digits after each intermediate calculation step. 4.12 Hand 4.14 Hand 4.15 Matlab Evaluate the remainder term in the Taylor series at x = 2 to estimate t E 4.21 Matlab Answers 4.1 First number is 89 Second number is 6.15625 4.3 >> macheps ans = 2.2204e-016 >> eps ans = 2.2204e-016 4.4 4.9407e-324 (or any extremely small value on the order of e-320 – solution may vary slightly from one
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Unformatted text preview: computer to the next) 4.7 True value: f (0.577) = 2,352,911 3-digit result with chopping: f (0.577) = 216,250, t = 90.8% 4-digit result with chopping: f (0.577) = 2,048,521, t = 12.9% 2 4.12 True value: f (3) = 554 Zero order: f (3) -62, t = 111.19% First order: f (3) 78, t = 85.92% Second order: f (3) 354, t = 36.10% Third order: f (3) 554, t = 0% 4.14 True value: f (2) = 0.693147. .. Zero order: f (2) = 0, t = 100% First order: f (2) = 1, t = 44.27% Second order: f (2) = 0.5, t = 27.87% Third order: f (2) 0.833333, t = 20.22% Fourth order: f (2) 0.583333, t = 15.84% 4.15 True value: f (2) = 283 Forward: f (2) = 312.8, t E = 29.8 Backward: f (2) = 255.2, t E = 27.8 Centrered: f (2) = 284, t E = 1 t E based on remainder term in Taylor series: Forward: t E = 28.8 Backward: t E = 28.8 Centrered: t E = 1 4.21...
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This note was uploaded on 09/05/2011 for the course EGM 3344 taught by Professor Raphaelhaftka during the Spring '09 term at University of Florida.

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HW_Assignment_2 - computer to the next) 4.7 True value: f...

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