assignment5.pdf - MATH-UA.0252(NYU Courant Spring 2019...

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MATH-UA.0252 (NYU Courant) Spring 2019: Numerical Analysis Assignment 5 (due May 3, 2019) Please see the helpful hints at the bottom of the homework. Also, try the Matlab publish command to print out your code along with the output. For all Matlab calculations and plots you do, please turn in your code. 1. [Space of polynomials P n , 1+2+2pts] Let P n be the space of functions defined on [ - 1 , 1] that can be described by polynomials of degree less of equal to n with coefficients in R . P n is a linear space in the sense of linear algebra, in particular, for p, q P n and a R , also p + q and ap are in P n . Since the monomials { 1 , x, x 2 , . . . , x n } are a basis for P n , the dimension of that space is n + 1 . (a) Show that for pairwise distinct points x 0 , x 1

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