1. Let A be the n x n Hilbert matrix with entries 1 %3D i+j Hilbert matrices are symmetric Hankel matrices which are theoretically positive definite, but very ill-conditioned. (a) Let y(n) = log,, K(A). Compute y(n) for n = 3:12 and determine a simple linear formula which will approximate y(n) for any n in that range. (b) Using the rank command, find the smallest n for which A is numerically singular.k
1. Let A be the n x n Hilbert matrix with entries 1 %3D i+j Hilbert matrices are symmetric Hankel matrices which are theoretically positive definite, but very ill-conditioned. (a) Let y(n) = log,, K(A). Compute y(n) for n = 3:12 and determine a simple linear formula which will approximate y(n) for any n in that range. (b) Using the rank command, find the smallest n for which A is numerically singular.k
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. Let A be the n x n Hilbert matrix with entries
1
%3D
i+j
Hilbert matrices are symmetric Hankel matrices which are theoretically positive
definite, but very ill-conditioned. (a) Let y(n) = log,, K(A). Compute y(n) for n =
3:12 and determine a simple linear formula which will approximate y(n) for any n in
that range. (b) Using the rank command, find the smallest n for which A is
numerically singular.-
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