Orthonormal high-level canonical PWL functions with applications to model reduction

This paper is the natural sequel to [1], An inner product is defined for th e linear vector space PWLH [S] of all the piecewise linear (PWL) continuous mappings defined over a rectangular compact set S, using a simplicial part ition H. This permits us to assure that PWLH [S] is a Hilbert space. Then, the notion of orthogonality is introduced and orthonormal bases of PWL func tions are formulated. A relevant consequence of the approach is that the pr oblem of function approximation can be translated to the more studied field of approximation in Hilbert spaces of finite dimension. As will be shown, this powerful theoretical framework can be used to generate an optimal sche me for model reduction.