In this paper, we develop a matrix framework to solve the problem of finding orthonormal rational function vectors with prescribed poles yk,l ∈ C, with respect to a certain discrete inner product that is defined by a set of data points zi,j ∈ C and corresponding weight vectors ~ wi,j . Our algorithm for solving the problem is recursive, and it is of complexity O(n). If all data points are real ...

This paper presents an overview about predictive control schemes based on orthonormal basis function models. Different predictive control schemes based on such models are discussed, namely, linear controllers with terminal (stabilizing) constraints, robust controllers, and non-linear controllers. The discussions comprise a broad bibliographical survey on the subject as well as two case studies ...

In this paper, we study the properties of the transform which approximates a signal at a given resolution. We show that the difference of a signal at different resolutions can be extracted by decomposing the signal on a wavelet orthonormal basis. In wavelet orthonormal basis is a family of functions, which is built by dilating and translating a unique function. The development of orthonormal wa...

Suppose that {ek} is an orthonormal basis for a separable, infinite-dimensional Hilbert space H. Let D be a diagonal operator with respect to the orthonormal basis {ek}. That is, D = ∑∞ k=1 λkek⊗ek, where {λk} is a bounded sequence of complex numbers. Let T = D + u1 ⊗ v1 + · · ·+ un ⊗ vn. Improving a result [2] of Foias et al., we show that if the vectors u1, . . . , un and v1, . . . , vn satis...

In this paper the implementation of Kogbetliantz's SVD algorithm using orthonormal {rotations is presented. An orthonormal {rotation is a rotation by an angle of a given set of {rotation angles (e.g. the angles i = arctan 2 ?i) which are choosen such that the rotation can be implemented by a small amount of shift{add operations. All computations (evaluation and application of the rotations) can...

Abstract Linear systems of differential equations with an invariant in the form a positive definite quadratic real Hilbert space are considered. It is assumed that system has simple spectrum and eigenvectors complete orthonormal system. Under these assumptions, linear can be represented Schrödinger equation by introducing suitable complex structure. As example, we present such representation fo...

This study considers a class of double finite Hankel transforms that describes the transmission of a vortex optical signal through a two-lens system with limited aperture radii in the object and spectral flats. The eigenfunctions of the given transform are calculated for different orders of vortex m. The functions obtained are an orthonormal system of functions, which can help expand an unspeci...