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A global analysis of Newton iterations for determining turning points

Vladimír Janovský, Viktor Seige (1993)

Applications of Mathematics

The global convergence of a direct method for determining turning (limit) points of a parameter-dependent mapping is analysed. It is assumed that the relevant extended system has a singular root for a special parameter value. The singular root is clasified as a $b i f u r c a t i o n s i n g u l a r i t y$ (i.e., as a $d e g e n e r a t e$ turning point). Then, the Theorz for Imperfect Bifurcation offers a particular scenario for the split of the singular root into a finite number of regular roots (turning points) due to a given parameter imperfection. The relationship...

A Remark on the Paper of H. H. Schaefer. Abschätzung der nichttrivalen Eigenwerte stochastischer Matrizen.

A. BRAUER (1971)

Numerische Mathematik

A two-stage Newton-like method for computing simple bifurcation points of nonlinear equations depending on two parameters

Gerd Pönisch (1990)

Banach Center Publications

Chord Techniques and Newton's Method for Discrete Bifurcation Problems.

E. Bohl (1980)

Numerische Mathematik

Computation of the Smallest Positive Eigenvalue of a Quadratic ..-matrix.

Rainer Garus, Tassilo Küpper (1990)

Numerische Mathematik

Continuation of invariant subspaces via the Recursive Projection Method

Vladimír Janovský, O. Liberda (2003)

Applications of Mathematics

The Recursive Projection Method is a technique for continuation of both the steady states and the dominant invariant subspaces. In this paper a modified version of the RPM called projected RPM is proposed. The modification underlines the stabilization effect. In order to improve the poor update of the unstable invariant subspace we have applied subspace iterations preconditioned by Cayley transform. A statement concerning the local convergence of the resulting method is proved. Results of numerical...

Effective methods for computing turning points of curves implicitly defined by nonlinear equations

Hubert Schwetlick (1984)

Banach Center Publications

Eine Abschätzung der nichttrivialen Eigenwerte stochastischer Matrizen.

H.H. SCHAEFER (1970)

Numerische Mathematik

How to Get around a Simple Quadratic Fold.

F. Brezzi, M. Cornalba, A. Di Carlo (1986)

Numerische Mathematik

Nonlinear elliptic boundary value problems versus their finite difference approximations: numerically irrelevant solutions.

K. Schmitt, H.O. Peitgen, D. Saupe (1981)

Journal für die reine und angewandte Mathematik

Pseudo-bosons from Landau levels.

Bagarello, Fabio (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Remark to the problem of eigenvalues of Schrödinger equation

Ivan Úlehla, Jan Wiesner (1970)

Aplikace matematiky

Stationary Schrödinger equations governing electronic states of quantum dots in the presence of spin-orbit splitting

Marta M. Betcke, Heinrich Voss (2007)

Applications of Mathematics

In this work we derive a pair of nonlinear eigenvalue problems corresponding to the one-band effective Hamiltonian accounting for the spin-orbit interaction governing the electronic states of a quantum dot. We show that the pair of nonlinear problems allows for the minmax characterization of its eigenvalues under certain conditions which are satisfied for our example of a cylindrical quantum dot and the common InAs/GaAs heterojunction. Exploiting the minmax property we devise an efficient iterative...