Results 61 to 70 of about 98,636 (202)

Convergence Results on Iteration Algorithms to Linear Systems

The Scientific World Journal, 2014
In order to solve the large scale linear systems, backward and Jacobi iteration algorithms are employed. The convergence is the most important issue. In this paper, a unified backward iterative matrix is proposed.
Zhuande Wang, Chuansheng Yang, Yubo Yuan
doaj   +1 more source

A new Jacobi wavelets decomposition method for solving partial differential equations [PDF]

Arab Journal of Mathematical Sciences
PurposeThe paper proposes a new spectral method based on Jacobi wavelets for numerically solving partial differential equations (PDEs).Design/methodology/approachThe authors used Jacobi wavelets as basis functions and employed the operational matrix of ...
Bahri Mohammed Nadjib, Sidi Mohammed Bahri   +1 more
doaj   +1 more source

Meromorphic continuations of finite gap Herglotz functions and periodic Jacobi matrices

, 2013
We find a necessary and sufficient condition for a Herglotz function $m$ to be the Borel transform of the spectral measure of an exponentially decaying perturbation of a periodic Jacobi matrix. The condition is in terms of meromorphic continuation of $m$
Kozhan, Rostyslav
core   +1 more source

Finite Biorthogonal Polynomials Suggested by the Finite Orthogonal Polynomials Mnp,qx$$ {M}_n^{\left(p,q\right)}(x) $$

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT Constructing a biorthogonal structure from scratch, that is, defining a biorthogonal pair is quite tough. Because here the orthogonality must be established between two different sets. There are four known univariate biorthogonal polynomial sets, suggested by Laguerre, Jacobi, Hermite and Szegő‐Hermite polynomials, in the literature.
Esra Güldoğan Lekesiz
wiley   +1 more source

The Spectral Connection Matrix for Any Change of Basis within the Classical Real Orthogonal Polynomials

Mathematics, 2015
The connection problem for orthogonal polynomials is, given a polynomial expressed in the basis of one set of orthogonal polynomials, computing the coefficients with respect to a different set of orthogonal polynomials.
Tom Bella, Jenna Reis
doaj   +1 more source

Optimal Homogeneous ℒp$$ {\boldsymbol{\mathcal{L}}}_{\boldsymbol{p}} $$‐Gain Controller

International Journal of Robust and Nonlinear Control, EarlyView.
ABSTRACT Nonlinear ℋ∞$$ {\mathscr{H}}_{\infty } $$‐controllers are designed for arbitrarily weighted, continuous homogeneous systems with a focus on systems affine in the control input. Based on the homogeneous ℒp$$ {\mathcal{L}}_p $$‐norm, the input–output behavior is quantified in terms of the homogeneous ℒp$$ {\mathcal{L}}_p $$‐gain as a ...
Daipeng Zhang, Benjamin Calmbach, Jaime A. Moreno, Johann Reger   +3 more
wiley   +1 more source

The Hahn-Exton q-Bessel function as the characteristic function of a Jacobi matrix

Special Matrices, 2014
A family T(ν), ν ∈ ℝ, of semiinfinite positive Jacobi matrices is introduced with matrix entries takenfrom the Hahn-Exton q-difference equation. The corresponding matrix operators defined on the linear hullof the canonical basis in ℓ2(ℤ+) are essentially
Štampach F., Šťovíček P.
doaj   +1 more source

An operational approach for solving fractional pantograph differential equation [PDF]

Iranian Journal of Numerical Analysis and Optimization, 2019
The aim of the current paper is to construct the shifted fractional-order Jacobi functions (SFJFs) based on the Jacobi polynomials to numerically solve the fractional-order pantograph differential equations. To achieve this purpose, first the operational
H. Ebrahimi, K. Sadri
doaj   +1 more source

Optimal Gain Selection for the Arbitrary‐Order Homogeneous Differentiator

International Journal of Robust and Nonlinear Control, EarlyView.
ABSTRACT Differentiation of noisy signals is a relevant and challenging task. Widespread approaches are the linear high‐gain observer acting as a differentiator and Levant's robust exact differentiator with a discontinuous right‐hand side. We consider the family of arbitrary‐order homogeneous differentiators, which includes these special cases.
Benjamin Calmbach, Jaime A. Moreno, Johann Reger   +2 more
wiley   +1 more source

The study of Jacobi and cyclic Jacobi matrix eigenvalue problems using Sturm–Liouville theory

Linear Algebra and its Applications, 2011
\textit{Q. Kong} et al. [J. Math. Anal. Appl. 263, No. 2, 748--762 (2001; Zbl 1001.34019)] discovered a class of Sturm-Liouville problems (SLPs) whose spectrum is a finite set of eigenvalues and earlier in [Result. Math. 54, No. 1-2, 103--116 (2009; Zbl 1185.34032)], the authors and \textit{H. Volkmer} obtained matrix representations of these problems.
Kong, Qingkai, Zettl, Anton
openaire   +1 more source