integral inner product vs dot product

Discussion in 'Undergraduate Math' started by Krille, Feb 18, 2004.

  1. Krille

    Krille Guest

    Suppose I want to do a least square approximation with the simple basis
    functions 1,t,t^2,...,t^(N-1). I choose a time grid as
    t=[0,1/(M-1),2/(M-1),...1]. This gives me a MxN matrix, say A. The basis
    functions phi_n(t)=t^n are polynomials and therefore I use the ususal
    integral inner product in (0,1).

    The inner product becomes smaller and smaller when m,n->M but of course it
    is not zero for any n,m. Does this prove that the columns becomes more
    linear dependent as n,m->M?

    What if I evaluate the matrix for the gridpoints and then use the "sum of
    squares" dot product to measure ortogonality between columns?
    Krille, Feb 18, 2004
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