2.1. Annxn Hilbert matrix, A, is defined by aij=1/(i+j-1) for i, j = 1, 2, ...,...

 

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2.1. Annxn Hilbert matrix, A, is defined by aij=1/(i+j-1) for i, j = 1, 2, ..., n Find the inverse of A and the inverse of ATA for n = 5. Then, noting that (ATA)=A (A-1)T find the inverse of ATA using this result for values of n = 3, 4, ..., 6. Compare the accuracy of the two results by using the inverse Hilbert function invhilb to find the exact inverse using (ATA)-1=A-(A-1). Hint: Compute norm(PR) and norm(QR) where P = (ATA)- and Q=A-(A-1)T and R is the exact value of Q. 2.2. Find the condition number of ATA where A is an n x n Hilbert matrix, defined in Problem 2.1, for n=3, 4, ..., 6. How do these results relate to the results of Problem 2.1? 2.1. Annxn Hilbert matrix, A, is defined by aij=1/(i+j-1) for i, j = 1, 2, ..., n Find the inverse of A and the inverse of ATA for n = 5. Then, noting that (ATA)=A (A-1)T find the inverse of ATA using this result for values of n = 3, 4, ..., 6. Compare the accuracy of the two results by using the inverse Hilbert function invhilb to find the exact inverse using (ATA)-1=A-(A-1). Hint: Compute norm(PR) and norm(QR) where P = (ATA)- and Q=A-(A-1)T and R is the exact value of Q. 2.2. Find the condition number of ATA where A is an n x n Hilbert matrix, defined in Problem 2.1, for n=3, 4, ..., 6. How do these results relate to the results of Problem 2.1?

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Solution to 21 and 22 Hilbert Matrix Inverse and Condition Number 21 Inverse of A AA and AT A1 Findi... View the full answer