## 2. Rayleigh-Ritz procedure (cont'd)

Recall that we wish to find the \(w(\mathbf{x})\) which
minimizes the energy functional \(F(w)\).

Since
$w=\sum _{i=1}^{n}{c}_{i}{w}_{i}$,
\(F(w)\) is now a function of the \(c_i\).

Minimizing \(F(w)\) over the set of linear combinations
of the basis functions
corresponds to choosing the \(c_i\) such that \(F\)
is minimal. Thus, we take the partial derivative of \(F\) with
respect to each \(c_i\) in turn and set it to zero.

R. Funnell
Last modified: 2018-11-07 12:52:06
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