numerical linear algebra

The three main problems of numerical linear algebra are: solving linear systems, solving eigenvalue/eigenvector problems, solving the linear least squares problem

On the convergence of the Newton-GMBACK method

6 years ago

AbstractWhen the GMBACK solver is used in the Newton iterates, the iterates may be written either as inexact Newton iterates…

A Chebyshev-Galerkin method for fourth order problems

7 years ago

AbstractWe study the linear stability of some Marangoni flows (thin films) on an inclined plane. The Orr-Sommerfeld eigenproblem contains two…

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

7 years ago

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

7 years ago

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

The inexact, inexact perturbed and quasi-Newton methods are equivalent models

8 years ago

Abstract A classical model of Newton iterations which takes into account some error terms is given by the quasi-Newton method,…

On the superlinear convergence of the successive approximations method

8 years ago

Abstract The Ostrowski theorem is a classical result which ensures the attraction of all the successive approximations xk+1 = G(xk) near a fixed…

Inexact perturbed Newton methods and applications to a class of Krylov solvers

8 years ago

Abstract Inexact Newton methods are variant of the Newton method in which each step satisfies only approximately the linear system…

On the high convergence orders of the Newton-GMBACK methods

8 years ago

Abstract GMBACK is a Krylov solver for linear systems in \(\mathbb{R}^n\). We analyze here the high convergence orders (superlinear convergence)…

On a third order iterative method for solving polynomial operator equations

8 years ago

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

8 years ago

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…

numerical linear algebra

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