272 research outputs found
Discrete-time multi-scale systems
We introduce multi-scale filtering by the way of certain double convolution
systems. We prove stability theorems for these systems and make connections
with function theory in the poly-disc. Finally, we compare the framework
developed here with the white noise space framework, within which a similar
class of double convolution systems has been defined earlier
From approximating to interpolatory non-stationary subdivision schemes with the same generation properties
In this paper we describe a general, computationally feasible strategy to
deduce a family of interpolatory non-stationary subdivision schemes from a
symmetric non-stationary, non-interpolatory one satisfying quite mild
assumptions. To achieve this result we extend our previous work [C.Conti,
L.Gemignani, L.Romani, Linear Algebra Appl. 431 (2009), no. 10, 1971-1987] to
full generality by removing additional assumptions on the input symbols. For
the so obtained interpolatory schemes we prove that they are capable of
reproducing the same exponential polynomial space as the one generated by the
original approximating scheme. Moreover, we specialize the computational
methods for the case of symbols obtained by shifted non-stationary affine
combinations of exponential B-splines, that are at the basis of most
non-stationary subdivision schemes. In this case we find that the associated
family of interpolatory symbols can be determined to satisfy a suitable set of
generalized interpolating conditions at the set of the zeros (with reversed
signs) of the input symbol. Finally, we discuss some computational examples by
showing that the proposed approach can yield novel smooth non-stationary
interpolatory subdivision schemes possessing very interesting reproduction
properties
The wavelet-based theory of spatial naturally curved and twisted linear beams
The paper presents the wavelet-based discretization of the linearized finite-strain beam theory which assumes small displacements, rotations and strains but is capable of considering an arbitrary initial geometry and material behaviour. In the numerical solution algorithm, we base our derivations on the vector of strain measures as the only unknown functions in a finite element. In such a way the determination of the beam quantities does not require the differentiation. This is an important advantage which allows a wider range of shape functions. In the present paper, the classical polynomial interpolation is compared to scaling and wavelet function interpolations. The computational efficiency of the method is demonstrated by analyzing initially curved and twisted beams
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