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I've been asking a lot of questions about interpolation of functions using polynomials:

Approximate $f(t) = 1-|2t-5|$ in $[2,3]$ by $p\in P_2$ by using the least squares method

Approximate $f(x) = x^{1/3}$ by $p(x)$ of degree $\le 2$ that minimizes the error $E = (f(-1)-p(-1))^2 + \int_{-1}^1 (f(x)-p(x))^2 dx + (f(1)-p(1))^2$

Fitting points to curve $g(t) = \frac{100}{1+\alpha e^{-\beta t}}$ by thinking about projections and inner products

Find polynomial of smallest norm and of degree $\le 3$ for which $p(0) = 2$

And all the answer i've been receiving are based on calculus\, taking derivatives. However, I'm studying linear algebra numerical methods in the context of projections onto polynomial spaces and using orthogonal families of polynomials.

Do anyone know a book that treats interpolation, smallest norm finding and other related things in a linear algebra way?

Guerlando OCs
  • 6,584
  • Linear algebra books. – Arturo Magidin Apr 15 '19 at 22:39
  • I believe that I can clarify the problems that you are fighting. Before I can write a useful answer to some of your question I must know the following: Given a basis for a subspace in $\mathbb{R}^n$ can you apply Gram-Schmidt algorithm to compute an orthonormal basis with respect to the standard Euclidian inner product? Moreover, given an orthonormal basis, can you compute the orthogonal projection on a subspace. I think your difficulty lies in recognizing the correct subspace and the appropriate inner product to use in the different cases. If this is true, then I can give useful answers. – Carl Christian Apr 17 '19 at 12:08
  • @CarlChristian yes, I know how to compute graam schmidt and orthogonal projection. It'd be very very very helpful if you can write answers to my questions because I'm only receiving calculus based answers. Thank you so much!!!! – Guerlando OCs Apr 17 '19 at 14:56

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