midterm2review

# midterm2review - Week 11 Test this Friday Review Midterm...

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Week 11 - Test this Friday - Review

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Midterm Topics Chapters 4.2-7.2 (not 5.1) - Interpolation error - Estimating derivatives - Integration techniques - Matrix reductions
Midterm Topics Interpolation: Estimating derivatives: Integration techniques: -Theory -Richardson Extrapolation -Trapezoidal -Romberg Algorithm -Simpson's -Adaptive Simpson's -Gaussian Quadrature -Error Matrix reductions: -Naive -Scaled Partial Pivoting

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Midterm Topics For all the problems, f(x) = x * e x
Interpolation Error Theorem 2, page 158: |Error| < M*h n+1 /(4*(n+1)) n = degree of interpolation polynomial h = step size between points M = maximum of the (n+1)th derivative of the function in the range specified

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Interpolation Error What is my error bound for x*e x on the range [-1,2] using [-1,0,1,2] as my interpolation points? 4 points -> degree 3 -> n = 3 Derivatives increase, so M is at x=2 h=1 So, |Error|< (2+4)e 2 *1 4 /(4*4)
Interpolation Error What if we use two separate parts to interpolate: [-1,0] and [0,1,2]?

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midterm2review - Week 11 Test this Friday Review Midterm...

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