Methods of Newton and Newton-Krylov type

Book summaryLocal convergence results on Newton-type methods for nonlinear systems of equations are studied. Solving of large linear systems by…

Spectral methods in linear stability. Applications to thermal convection with variable gravity field

AbstractThe onset of convection in a horizontal layer of fluid heated from below in the presence of a gravity field…

On the numerical treatment of the eigenparameter dependent boundary conditions

AbstractIn this paper, we consider the numerical treatment of singular eigenvalue problems supplied with eigenparameter dependent boundary conditions using spectral…

On a third order iterative method for solving polynomial operator equations

Abstract We present a semilocal convergence result for a Newton-type method applied to a polynomial operator equation of degree (2).…

On approximating the eigenvalues and eigenvectors of linear continuous operators

Abstract We consider the computing of an eigenpair (an eigenvector $$v=(v^{(i)})_{i=1,n}$$ and an eigenvalue $$\lambda$$) of a matrix $$A\in\mathbb{R}^{n\times n}$$, by…

On the Chebyshev method for approximating the eigenvalues of linear operators

Abstract We study the approximation of an eigenpair (an eigenvalue and a corresponding eigenvector) of a a linear operator T from…

On some interpolatory iterative methods for the second degree polynomial operators (I)

Abstract In this note we consider the chord (secant) method and the Steffensen method for solving polynomial operators of degree…

Remarks on some Newton and Chebyshev-type methods for approximation eigenvalues and eigenvectors of matrices

Abstract We consider a square matrix $$A$$ with real or complex elements. We denote $$\mathbb{K}=\mathbb{R}$$ or $$\mathbb{C}$$ and we are…