ichbin
04-06-2014, 11:06 PM
At the beginning of section 10.8 on the conjugate gradient method, the text gives equation 10.8.1 for an N-dimensional quadratic form, and then states: "...the number of unknown parameters in f is equal to the number of free parameters in A and b, which is N(N+1)/2..."
The total number of parameters in an N-dimensional quadratic form is actually (N+1)(N+2)/2. For example, for N=2, A has 3 parameters, b two parameters, and c one, for a total of 6. In my opinion, the text should read: "...the number of unknown parameters in f is equal to the number of free parameters in A, b, and c, which is (N+1)(N+2)/2...".
Since the rest of the argument only depends on the result being ~N^2, this isn't a big deal, but given NR's status as a go-to reference, it would be nice to have this right.
The total number of parameters in an N-dimensional quadratic form is actually (N+1)(N+2)/2. For example, for N=2, A has 3 parameters, b two parameters, and c one, for a total of 6. In my opinion, the text should read: "...the number of unknown parameters in f is equal to the number of free parameters in A, b, and c, which is (N+1)(N+2)/2...".
Since the rest of the argument only depends on the result being ~N^2, this isn't a big deal, but given NR's status as a go-to reference, it would be nice to have this right.