Showing papers in "Filomat in 2003"
TL;DR: In this paper, a survey of recent research in the field of matrix transformations at the University of Ni s, Serbia and Montenegro, in the past four years is presented, where the authors give necessary and sufficient conditions for the entries of a matrix to map X into Y and characterize the subclass of matrices that are com- pact operators.
Abstract: Many important sequence spaces arise in a natural way from various concepts of summability, namely ordinary, absolute and strong summability In the rst two cases they may be considered as the domains of the matrices that dene the respective methods of summability; the situation, however, is dieren t and more complicated in the case of strong summa- bility Given sequence spaces X and Y , we nd necessary and suf- cien t conditions for the entries of a matrix to map X into Y , and characterize the subclass of those matrices that are com- pact operators This paper gives a survey of recent research in the eld of matrix transformations at the University of Ni s, Serbia and Montenegro, in the past four years
97 citations
TL;DR: In this paper, the authors give various properties and inclusion relations on these sequence spaces and show that they are lacunary if k 0 = 0, 0 < k r < kr+1, and hr = kr-kr-1 → ∞ as r → ǫ.
Abstract: A sequence Θ = (kr) of positive integers is called lacunary if k0 = 0, 0 < kr < kr+1 and hr = kr – kr-1 → ∞ as r → ∞. The intervals determined by Θ are denoted by Ir = (kr-1, kr]. Let ω be the set of all sequences of complex numbers and f be a modulus function. Then we define NΘ(Δm, f) = {x є ω: lim 1/hr Σ f(|Δm xk -l|)=0 for some l} r kєIr NΘ0(Δm, f) = {x є ω: lim 1/hr Σ f(|Δm xk|)=0} r kєIr NΘ∞(Δm, f) = {x є ω: sup 1/hr Σ f(|Δm xk|)< ∞} r kєIr where Δxk = xk - xk+1, Δmxk = Δm-1xk - Δm-1xk+1 and m is a fixed positive integer. In this study we give various properties and inclusion relations on these sequence spaces.
21 citations
TL;DR: In this article, a quadrature rule for the approximation of integration with respect to the measure of orthogonality for complex Jacobi matrices has been proposed and some interesting examples are presented.
Abstract: Given any sequence of orthogonal polynomials, satisfying the three term recurrence relation xpn(x) = βn+1pn+1(x) + αnpn(x) + βnpn-1(x), p-1(x)=0 po(x)=1 with βn ≠ 0, n є N, β0 = 1, an infinite Jacobi matrix can be associated in the following way ┌ ┐ │α0 β1 0...│ │ │ │β1 α1 β2...│ │ │ J = │0 β2 α2...│ │.... │ │.... │ │....│ └ ┘ In the general case if the sequences {αn} or {βn} are complex the associated Jacobi matrix is complex. Under the condition that both sequences {αn}and {βn} are uniformly bounded, the associated Jacobi matrix can be understood as a linear operator J acting on l2, the space of all complex square-summable sequences, where the value of the operator J at the vector x is a product of an infinite vector x and an infinite matrix J in the matrix sense. The case when the sequences {αn} and {βn} are not uniformly bounded, an operator acting on l2 can not be defined that easily. Additional properties of the sequence of orthogonal polynomials are needed in order to be able to define the operator uniquely. The case when the sequences αn and βn are real is very well understood. The spectra of the Jacobi matrix J equals the support of the measure of orthogonality for the given sequence of orthogonal polynomials. All zeros of orthogonal polynomials are real, simple and interlace, contained in the convex hull of the spectra of the Jacobi operator associated with the infinite Jacobi matrix J. Every point in σ(J) attracts zeros of orthogonal polynomials. An application of orthogonal polynomials is the construction of quadrature rules for the approximation of integration with respect to the measure of orthogonality. For arbitrary sequences {αn} and {βn} the situation is changed dramatically. Zeros of orthogonal polynomials need not be simple; they are not real and they do not necessarily lie in the convex hull of σ(J). There is also a little known about convergence results of related quadrature rule. Only in recent years a connection between complex Jacobi matrices and related orthogonal polynomials is interesting again (see [2]). Studies of complex Jacobi operators should lead to a better understanding of related orthogonal polynomials, but also the study of orthogonal polynomials with the complex Jacobi matrices should put more light on the non-hermitian banded symmetric matrices. In this lecture some results are given about complex Jacobi matrices and related quadrature rules, and also some interesting examples are presented.
12 citations
TL;DR: The idea of difference sequence spaces was intro-duced by Kizmaz [9] and generalized by Et and Colak [6] as discussed by the authors, who introduced the sequence spaces [V, λ, f, p] 0 (Δr, E), [V λ 1, λ 2, f 1, p] ∞ (δr, E) where E is any Banach space, examine them and give various properties and inclusion relations on these spaces.
Abstract: The idea of difference sequence spaces was intro- duced by Kizmaz [9] and generalized by Et and Colak [6]. In this paper we introduce the sequence spaces [V, λ, f, p]0 (Δr, E), [V, λ, f, p]1 (Δr, E), [V, λ, f, p]∞ (Δr, E) Sλ (Δr, E) and Sλ0 (Δr, E) where E is any Banach space, examine them and give various properties and inclusion relations on these spaces. We also show that the space Sλ (Δr, E) may be represented as a [V, λ, f, p]1 (Δr, E)space.
11 citations
TL;DR: In this article, the authors introduce some new difference sequence spaces combining lacunary sequences and Orlicz functions, and establish some inclusion relations between these spaces, which are then used to define the difference sequence space.
Abstract: In this paper we introduce some new difference sequence spaces combining lacunary sequences and Orlicz functions. We establish some inclusion relations between these spaces.
8 citations
TL;DR: In this article, a characterization of matrix transformations in these spaces is given. But the results generalize those given in [11, 14, 16] and do not generalize the results given in this paper.
Abstract: In this paper we deal with matrix transformations mapping in either of the sets sα(Nq), sαo(Nq) or sα(c)(Nq). Then we study some properties of the sets sα(Np Nq) and sαo(Np Nq) and give a characterization of matrix transformations in these spaces. These results generalize those given in [11, 14, 16].
6 citations
TL;DR: This paper addresses the problem of rectangular matrix multiplication on bidirectional linear systolic arrays (SAs) and points out which SA is the best choice depending on the relation between matrix dimensions.
Abstract: This paper addresses the problem of rectangular matrix multiplication on bidirectional linear systolic arrays (SAs). We analyze all bidirectional linear SAs in terms of efficiency. We conclude that the efficiency depends on the relation between the loop boundaries in the systolic algorithm (i.e. matrix dimensions). We point out which SA is the best choice depending on the relation between matrix dimensions. We have designed bidirectional linear systolic arrays suitable for rectangular matrix multiplication.
5 citations
TL;DR: In this article, the authors considered the convergence of the Ehrlich-Aberth method for the simultaneous approximation of simple complex zeros of a polynomial and proved that this method has the order of convergence equals four.
Abstract: The fourth order methods for the simultaneous approximation of simple complex zeros of a polynomial are considered. The main attention is devoted to a new method that may be regarded as a modification of the well known cubically convergent Ehrlich-Aberth method. It is proved that this method has the order of convergence equals four. Two numerical examples are given to demonstrate the convergence behavior of the studied methods.
4 citations
TL;DR: In this article, the authors presented an iterative method of Weierstrass's type for the simultaneous inclusion of all multiple zeros of a polynomial, where the order of convergence of the proposed interval method is 1 + √ 2 ≈ 2.414 or 3, depending on the type of the applied disk inversion.
Abstract: In this paper we present iterative methods of Weierstrass's type for the simultaneous inclusion of all multiple zeros of a polynomial. The order of convergence of the proposed interval method is 1 + √2 ≈ 2.414 or 3, depending on the type of the applied disk inversion. The criterion for the choice of a proper circular root-set is given. This criterion uses the already calculated entries which increases the computational efficiency of the presented algorithms. Numerical results are given to demonstrate the convergence behavior.
4 citations
3 citations
TL;DR: A fractal interpolant of the proper interpolation data is fully determined by the functional equation of Read-Bejraktarevic type and a free vertical scaling vector such that ||ν|| < 1 as mentioned in this paper.
Abstract: A fractal interpolant of the proper interpolation data is fully determined by the functional equation of Read- Bejraktarevic type and a free vertical scaling vector ν such that ||ν|| < 1. In this note, it is shown how insertion of the data impacts the related Read-Bejraktarevic equation and the interpolant. Some examples support the theory.
TL;DR: In this article, the authors propose a method for optimization of polyno-mial representation of switching functions, which can be applied to arbitrary polynomial expressions providing that the corresponding transform matrix has the Kronecker product structure.
Abstract: Compact representations of switching functions pro- vide for simplied realizations of logic networks. Recent advent of digital technology and VLSI raised a considerable interest in polynomial expressions for switching functions. Complexity of these expressions is estimated through the number of product terms. For a given function and the selected class of polyno- mial expressions, the number of products can be reduced by a suitable selection of polarities for switching variables, which results in Fixed Polarity Polynomial Expressions (FPPEs). This paper proposes a method for optimization of polyno- mial representation of switching functions. The method ex- ploits the notion of dual polarity of switching variables and takes advantages of a simple relationship between two FPPEs for dual polarities. Calculation of FPPEs is performed along the extended dual polarity route so that each FPPE is calcu- lated from its extended dual polarity FPPE. Conversion from one FPPE to another is carried out by using one-bit check, which ensures the eciency of the method. The proposed method can be applied to arbitrary polynomial expressions providing that the corresponding transform matrix has the Kronecker product structure.
TL;DR: In this article, the problem of finding the first basic solution in the two phases simplex algorithm is analyzed, and a modification and several improvements of the simplex method are introduced.
Abstract: We analyze the problem of finding the first basic solution in the two phases simplex algorithm. Also, a modification and several improvements of the simplex method are introduced. We report computational results on numerical examples from Netlib test set.
TL;DR: In this article, a combined method for the simultaneous inclusion of complex zeros of a polynomial, composed of two circular arithmetic methods, is presented, and the order of convergence equals four.
Abstract: A combined method for the simultaneous inclusion of complex zeros of a polynomial, composed of two circular arithmetic methods, is presented. This method does not use polynomial derivatives and has the order of convergence equals four. Computationally variable initial conditions that guarantee the convergence are also stated. Two numerical example are included to demonstrate the convergence speed of the presented method.
TL;DR: In this paper, the authors give use of their own software for dierential geom- etry and geometry and its extensions (4, 3, 1, 5) and apply it to the visualisation and animation of isometries between certain surfaces.
Abstract: We give use our own software for dierential geom- etry and geometry and its extensions (4, 3, 1, 5) and apply it to the visualisation and animation of isometries between certain surfaces.