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 numerical treatment of the eigenparameter dependent boundary conditions

6 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

7 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

7 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

7 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

7 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

7 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

7 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…

On the Chebyshev method for approximating the eigenvalues of linear operators

7 years ago

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)

7 years ago

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

7 years ago

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

numerical linear algebra

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