hw4 - Homework 4 Math 104B Winter 2011 Due on Thursday...

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Homework 4 – Math 104B, Winter 2011 Due on Thursday, February 17th, 2011 Section 7.3: 17, 18, and 26. Section 7.4: 1d, 2b, 3d, and 4b. Additional problem: The n × n Hilbert matrix H ( n ) defined by H ( n ) ij = 1 i + j - 1 1 i, j n is an ill-conditioned matrix that arises in solving the normal equations for the coefficients of the least squares polynomials. a. Show that [ H (4) ] - 1 = 16 - 120 240 - 140 - 120 1200 - 2700 1680 240 - 2700 6480 - 4200 - 140 1680 - 4200 2800 b. For n = 20 and n = 100, pick the right hand side b so that the solution to H ( n ) x = b is the vector x = (1 , 2 , . . . , n ) (do this in your program, before calling your subroutine). Then solve the system of equations using Gauss Eliminations with Backward Substitution and compute the relative error in the solution. In order to do this, define the absolute error as: || x - y || = max {| x 1 - y 1 | , | x 2 - y 2 | , . . . , | x n - y n |} How good is the numerical solution obtained? Notes:
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This note was uploaded on 12/27/2011 for the course MATH 104b taught by Professor Ceniceros,h during the Fall '08 term at UCSB.

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hw4 - Homework 4 Math 104B Winter 2011 Due on Thursday...

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