# Numerical Analysis &amp; Interpolation

## Transcribed Text

This is to be a typed report. The matlab functions polyfit and polyval should be useful to you. 1. For each of the algorithms you will be using, write a description of the algorithm, what it is doing, and why. Write at a level in this question and, indeed, for all questions in this assignment and your other assignments in this class, so that a junior in college with the prerequisites for this class can understand what you are saying. 2. For each of the two functions on the interval [-1,1], and (x) - 1 25.2² 1 do the following. a. Find the interpolating polynomial at xj = + for j = 0,1 8. Graph each function on the same graph as the interpolating polynomial. b Find the interpolating polynomial at the zeros of the eighth degree Legendre polynomial. (The nodes and weights are in the paper linked to the web page. )Graph each function on the same graph as the interpolating polynomial. c. For each function f and g compute the integral from -1 to 1. d. Integrate each of the interpolating polynomials you found in a and b from -1 to 1. and compare your results to the integrals of f and g. How does this relate to Newton-Cotes quadrature and Gaussian quadrature. e. For the nodes above, give the composite trapezoid and composite Simpson's rule approximation of the integral. 3. Write a conclusion discussing what you found. 1

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