The Ritz Method

Abstract

As before, let A be a positive definite operator on a linear set D _A in a separable Hilbert space H, and let f ∈ H. Let H _A be the Hilbert space of Chap. 10 (thus separable because H is separable, see p. 146). In H _A consider a base (i.e., an at most countable linearly independent complete system)

$$ {{\varphi }_{1}},{{\varphi }_{2}}, \ldots {\text{ }}{\text{.}} $$

(13.1)