matlab - Calculating condition numbers for hilbert matrices -


okay, first off feel silly asking question since seems answer should simple can't figure out.

i have vector n: 

n=[2:13]

i pass vector through elementwise returns vector calculated values:

condition=cond(hilb(n))

hilb(n) returns hilbert matrix dimension n. cond() calculates condition number, scalar value. currently, matlab returning condition single value using first value n, 2 instead of vector equal in length n.

i aware of using .* , sin.() , other commands compute things elementwise, can't find how function such this.

you can't pass vector hilb that, unfortunately. should use loop, or simpler, arrayfun:

condition = arrayfun(@(x) cond(hilb(x)), n)

note arrayfun disguised loop, offers no performance benefit compared explicitly writing loop.

condition = zeros(1,numel(n)); ii = 1:numel(n)    condition(ii) = cond(hilb(n(ii))); end

keep in mind hilb ill-conditioned matrix, values high (cond(hilb(13))=8.3042e+19. means resulting vector like: 1.0e+19* 0.0000 0.0000 ... 0.0017 8.3042. if use format short e, you'll see values of each individual element: 1.9281e+01 5.2406e+02 ... 8.3042e+19.


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