Let qn Pn[-1,1], n = N, be the Chebyshev least squares polynomial for a given polynomial...

 

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Let qn Pn[-1,1], n = N, be the Chebyshev least squares polynomial for a given polynomial Pn+1 Pn+1[1,1]. Show that on coincides with the Lagrange interpola- tion polynomial for pm with respect to the Chebyshev nodes x0,x1,. ...,xn. Let qn Pn[-1,1], n = N, be the Chebyshev least squares polynomial for a given polynomial Pn+1 Pn+1[1,1]. Show that on coincides with the Lagrange interpola- tion polynomial for pm with respect to the Chebyshev nodes x0,x1,. ...,xn.