This short note provides an improvement on a recent result of Vecchio on a norm bound for the inverse of a lower triangular Toeplitz matrix with nonnegative entries. A sharper asymptotic bound is obtained as well as a version for matrices of finite order. The results are shown to be nearly best possible under the given constraints. 1. Introduction. This paper provides an improvement on a recent...

For any interpolatory ternary subdivision scheme with two-ring stencils for a regular triangular or quadrilateral mesh, in this paper we show that the critical Hölder smoothness exponent of its basis function cannot exceed log3 11(≈ 2.18266), where the critical Hölder smoothness exponent of a function f : R2 7→ R is defined to be ν∞(f) := sup{ν : f ∈ Lip ν}. On the other hand, for both regular ...

The space of upper triangular matrices with Hilbert{Schmidt norm can be viewed as a nite dimensional analogue of the Hardy space H2 of the unit disk when one introduces the adequate notion of \point" evaluation. A bitangential interpolation problem in this setting is studied. The description of all solution in terms of Beurling{Lax representation is given.

Let A and B be bounded linear operators acting on a Hilbert space H. It is shown that the triangular inequality serves as the ultimate estimate of the upper norm bound for the sum of two operators in the sense that sup{‖U∗AU + V ∗BV ‖ : U and V are unitaries} = min{‖A+ μI‖+ ‖B − μI‖ : μ ∈ C}. Consequences of the result related to spectral sets, the von Neumann inequality, and normal dilations a...

For any interpolatory ternary subdivision scheme with two-ring stencils for a regular triangular or quadrilateral mesh, we show that the critical Hölder smoothness exponent of its basis function cannot exceed log3 11(≈ 2.18266), where the critical Hölder smoothness exponent of a function f : R2 → R is defined to be ν∞(f) := sup{ν : f ∈ Lip ν}. On the other hand, for both regular triangular and ...

In this paper, a multigrid algorithm is developed for the third-order accurate solution of Cauchy–Riemann equations discretized in the cell-vertex finite-volume fashion: the solution values stored at vertices and the residuals defined on triangular elements. On triangular grids, this results in a highly overdetermined problem, and therefore we consider its solution that minimizes the residuals ...

This paper presents new image processing operations based on the Dubois and Prade proposal of a fuzzy triangular norm. This definition is recalled, and a computational efficient algorithm is derived for its fast computation. This procedure also gives a comprehensive model for reasoning about the qualitative effects of the Dubois and Prade fuzzy norm on data. The presented image processing opera...

Scaled iterates associated with the serial Kogbetliantz method for computing the singular value decomposition (SVD) of complex triangular matrices are considered. They are defined by B (k) S = |diag(B )| B |diag(B)|, where B are matrices generated by the method. Sharp estimates are derived for the Frobenius norm of the off-diagonal part of B (k) S , in the case of simple singular values. This n...

Triangular norms (t-norms for short) play a crucial role in several fields of mathematics and AI. For an exhaustive overview on t-norms we refer to [20]. Recently an increasing interest of left-continuous t-norm based theories can be observed (see e.g. [3, 5, 6, 7, 18]). In this paper we discuss in detail the presently existing construction methods which result in left-continuous triangular nor...

Triangular norms in the study of probabilistic metric spaces as a special kind of associative functions defined on the unit interval. These functions have found applications in many areas since then. In this study, we present new methods for constructing triangular norms and triangular conorms on an arbitrary bounded lattice under some constraints. Also, we give some illustrative examples for t...