Finite Dimensional LVS

Polynomials of deg \(\leq 7\) foo foo cachoo foo

b-spline interpolation

\(\mathcal{X} = span(\phi_1, .., \phi_n)\)

\(\phi_n = b(t - n)\) where n is the spline order

• \(b_0(t) = \begin{cases} 1, & |t| \leq 1/2 \\ 0, & else \end{cases}\)
• \(b_1 = b_0 \ast b_0\)
• . . .
• \(b_n = b_0 \ast b_{n-1}\)