ABSTRACT
In the previous section we always assumed that M 1 ⊂ M 2 ⊂…⊂ MJ ≡ M. Thus the inner product (·,·) and the form A(·,·) defined on M are defined on Mk for any k. In some applications it is useful to not restrict ourselves to this case. Thus we want to allow the spaces Mk to be not necessarily nested and also we want to be able to define, for each k, a form Ak (·,·) and an inner product (·,·) k . We will follow as closely as possible the development in Section 3 but introducing now the more general framework. We recall that our goal is always to define an algorithm for the construction of an operator BJ : M → M which can be used to define a linear iterative process for solving (1.1) or a preconditioner for A.
