Search results for "Numerical Analysis"
showing 10 items of 883 documents
A note on k-generalized projections
2007
Abstract In this note, we investigate characterizations for k -generalized projections (i.e., A k = A ∗ ) on Hilbert spaces. The obtained results generalize those for generalized projections on Hilbert spaces in [Hong-Ke Du, Yuan Li, The spectral characterization of generalized projections, Linear Algebra Appl. 400 (2005) 313–318] and those for matrices in [J. Benitez, N. Thome, Characterizations and linear combinations of k -generalized projectors, Linear Algebra Appl. 410 (2005) 150–159].
Fractional Laplacians in bounded domains: Killed, reflected, censored, and taboo Lévy flights.
2018
The fractional Laplacian $(- \Delta)^{\alpha /2}$, $\alpha \in (0,2)$ has many equivalent (albeit formally different) realizations as a nonlocal generator of a family of $\alpha $-stable stochastic processes in $R^n$. On the other hand, if the process is to be restricted to a bounded domain, there are many inequivalent proposals for what a boundary-data respecting fractional Laplacian should actually be. This ambiguity holds true not only for each specific choice of the process behavior at the boundary (like e.g. absorbtion, reflection, conditioning or boundary taboos), but extends as well to its particular technical implementation (Dirchlet, Neumann, etc. problems). The inferred jump-type …
Qualitative analysis of matrix splitting methods
2001
Abstract Qualitative properties of matrix splitting methods for linear systems with tridiagonal and block tridiagonal Stieltjes-Toeplitz matrices are studied. Two particular splittings, the so-called symmetric tridiagonal splittings and the bidiagonal splittings, are considered, and conditions for qualitative properties like nonnegativity and shape preservation are shown for them. Special attention is paid to their close relation to the well-known splitting techniques like regular and weak regular splitting methods. Extensions to block tridiagonal matrices are given, and their relation to algebraic representations of domain decomposition methods is discussed. The paper is concluded with ill…
A Property on Singularities of NURBS Curves
2002
We prove that if a.n open Non Uniform Rational B-Spline curve of order k has a singular point, then it belongs to both curves of order k - 1 defined in the k - 2 step of the de Boor algorithm. Moreover, both curves are tangent at the singular point.
Superstable cycles for antiferromagnetic Q-state Potts and three-site interaction Ising models on recursive lattices
2013
We consider the superstable cycles of the Q-state Potts (QSP) and the three-site interaction antiferromagnetic Ising (TSAI) models on recursive lattices. The rational mappings describing the models' statistical properties are obtained via the recurrence relation technique. We provide analytical solutions for the superstable cycles of the second order for both models. A particular attention is devoted to the period three window. Here we present an exact result for the third order superstable orbit for the QSP and a numerical solution for the TSAI model. Additionally, we point out a non-trivial connection between bifurcations and superstability: in some regions of parameters a superstable cyc…
Eigenvalues of non-hermitian matrices: a dynamical and an iterative approach. Application to a truncated Swanson model
2020
We propose two different strategies to find eigenvalues and eigenvectors of a given, not necessarily Hermitian, matrix (Formula presented.). Our methods apply also to the case of complex eigenvalues, making the strategies interesting for applications to physics and to pseudo-Hermitian quantum mechanics in particular. We first consider a dynamical approach, based on a pair of ordinary differential equations defined in terms of the matrix (Formula presented.) and of its adjoint (Formula presented.). Then, we consider an extension of the so-called power method, for which we prove a fixed point theorem for (Formula presented.) useful in the determination of the eigenvalues of (Formula presented…
Derivatives not first return integrable on a fractal set
2018
We extend to s-dimensional fractal sets the notion of first return integral (Definition 5) and we prove that there are s-derivatives not s-first return integrable.
Resonances for nonanalytic potentials
2009
We consider semiclassical Schr"odinger operators on $R^n$, with $C^infty$ potentials decaying polynomially at infinity. The usual theories of resonances do not apply in such a non-analytic framework. Here, under some additional conditions, we show that resonances are invariantly defined up to any power of their imaginary part. The theory is based on resolvent estimates for families of approximating distorted operators with potentials that are holomorphic in narrow complex sectors around $R^n$.
On the accurate determination of nonisolated solutions of nonlinear equations
1981
A simple but efficient method to obtain accurate solutions of a system of nonlinear equations with a singular Jacobian at the solution is presented. This is achieved by enlarging the system to a higher dimensional one whose solution in question is isolated. Thus it can be computed e. g. by Newton's method, which is locally at least quadratically convergent and selfcorrecting, so that high accuracy is attainable.
Quadrature Formula Based on Interpolating Polynomials: Algorithmic and Computational Aspects
2007
The aim of this article is to obtain a quadrature formula for functions in several variables and to analyze the algorithmic and computational aspects of this formula. The known information about the integrand is {λi(f)}i=1n, where λi are linearly independent linear functionals. We find a form of the coefficients of the quadrature formula which can be easy used in numerical calculations. The main algorithm we use in order to obtain the coefficients and the remainder of the quadrature formula is based on the Gauss elimination by segments method. We obtain an expression for the exactness degree of the quadrature formula. Finally, we analyze some computational aspects of the algorithm in the pa…