http://i45.tinypic.com/2mo10me.png
The inner product here is defined by the integration of p(x)q(x) from 0 to 1.
I sort of understand why this is true, but I can't prove it (so I guess I don't fully understand it).
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http://i45.tinypic.com/2mo10me.png
The inner product here is defined by the integration of p(x)q(x) from 0 to 1.
I sort of understand why this is true, but I can't prove it (so I guess I don't fully understand it).
Quote:
Originally Posted by davismj
Google "Gram-Schmidt orthogonal basis"
Tonio
I know how to do a Gram-Schmidt procedure. What I don't understand is how to show that the matrix for the differentiation operator on the orthonormal basis (1,sqrt(3)(2x-1),sqrt(5)(6x^2-6x+1)) is upper triangular...
Quote:
Originally Posted by davismj
Why did you choose precisely that basis for? Check that wrt the basis
, the matrix of the diff. operator ALREADY is upper triangular, so just carry on the GS process on this basis...
Tonio