4 results
Search Results
Now showing 1 - 4 of 4
Conference Object Inverse Spectral Problems for Complex Jacobi Matrices(Springer New York LLC, 2013) Guseinov,G.S.The paper deals with two versions of the inverse spectral problem for finite complex Jacobi matrices. The first is to reconstruct the matrix using the eigenvalues and normalizing numbers (spectral data) of the matrix. The second is to reconstruct the matrix using two sets of eigenvalues (two spectra), one for the original Jacobi matrix and one for the matrix obtained by deleting the last row and last column of the Jacobi matrix. Uuniqueness and existence results for solution of the inverse problems are established and an explicit procedure of reconstruction of the matrix from the spectral data is given. It is shown how the results can be used to solve finite Toda lattices subject to the complex-valued initial conditions. © Springer Science+Business Media New York 2013.Conference Object Itô–taylor Expansions for Systems of Stochastic Differential Equations With Applications To Stochastic Partial Differential Equations(Springer New York LLC, 2017) Yılmaz,F.; Öz Bakan,H.; Weber,G.-W.Stochastic differential equations (SDEs) are playing a growing role in financial mathematics, actuarial sciences, physics, biology and engineering. For example, in financial mathematics, fluctuating stock prices and option prices can be modeled by SDEs. In this chapter, we focus on a numerical simulation of systems of SDEs based on the stochastic Taylor series expansions. At first, we apply the vector-valued Itô formula to the systems of SDEs, then, the stochastic Taylor formula is used to get the numerical schemes. In the case of higher dimensional stochastic processes and equations, the numerical schemes may be expensive and take more time to compute. We deal with systems with standard n-dimensional systems of SDEs having correlated Brownian motions. One the main issue is to transform the systems of SDEs with correlated Brownian motions to the ones having standard Brownian motion, and then, to apply the Itô formula to the transformed systems. As an application, we consider stochastic partial differential equations (SPDEs). We first use finite difference method to approximate the space variable. Then, by using the stochastic Taylor series expansions we obtain the discrete problem. Numerical examples are presented to show the efficiency of the approach. The chapter ends with a conclusion and an outlook to future studies. © 2017, Springer International Publishing AG.Article Citation - Scopus: 2Wong’s Oscillation Theorem for the Second-Order Delay Differential Equations(Springer New York LLC, 2017) Özbekler,A.; Zafer,A.[No abstract available]Conference Object Non-Asymptotic Norm Estimates for the Q-Bernstein Operators(Springer New York LLC, 2013) Ostrovska,S.; Özban,A.Y.The aim of this paper is to present new non-asymptotic norm estimates in C[0,1] for the q-Bernstein operators Bn,q in the case q > 1. While for 0 < q ≤ 1, {double pipe}Bn,q{double pipe} = 1 for all n ∈ ℕ, in the case q > 1, the norm {double pipe}Bn,q{double pipe} grows rather rapidly as n → + ∞ and q → + ∞. Both theoretical and numerical comparisons of the new estimates with the previously available ones are carried out. The conditions are determined under which the new estimates are better than the known ones. © Springer Science+Business Media New York 2013.
