MTH 510 - Lab 2 - Fall 2012 Example 1 - Matlab if and case ...
MTH 510 - Lab 2 - Fall 2012 Example 1 - Matlab if and case ...
MTH 510 - Lab 2 - Fall 2012 Example 1 - Matlab if and case ...
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<strong>MTH</strong> <strong>510</strong> - <strong>Lab</strong> 2 - <strong>Fall</strong> 2013<strong>Example</strong> 1 - <strong>Matlab</strong> <strong>if</strong> <strong>and</strong> <strong>case</strong> structuresDue to floating-point errors, computing the roots of the quadratic equationby means of the st<strong>and</strong>ard quadratic formulaax 2 + bx + c = 0 (1)x 1,2 = −b ± √ b 2 − 4ac2amay not always be the best way to compute them. In particular, <strong>if</strong> 4|ac| ≪ b 2 , better expressions arex 1 = − b + √ b 2 − 4ac2ax 1 = −b + √ b 2 − 4ac, x 2 =2a2c, x 2 = −b + √ , <strong>if</strong> b > 0,b 2 − 4ac(2)2c−b + √ b 2 − 4ac , <strong>if</strong> b < 0,These formulas can be derived by rationalizing the numerator in the root that leads to the biggest error.Write an M-file to compute the roots of (1) using (2) for the <strong>case</strong> when 4|ac| < b 2 . For values of a, b, c outsidethis range, output the comment “a,b,c outside range for this example”. Test your function for the equationusing MATLAB’s double precision format.x 2 + 9 12 x = 3<strong>Example</strong> 2 - Other <strong>Matlab</strong> Structures - Brief DemoFor loops:for i=1:0.1:3disp(i)endWhile structure:x=1while (x
Exercise (Problem 4.4)Using double precision, write an M-file to determine the machine espilon based on the following algorithm:Step 1: Set ɛ = 1Step 2: If 1 + ɛ is less than or equal to 1, then go to Step 5. Otherwise go to Step 3.Step 3: ɛ = ɛ/2Step 4: Return to Step 2.Step 5: ɛ = 2 ∗ ɛCompare your result with the value returned from the built-in eps function.2
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