O řešení soustavy nelineárních rovnic s funkční maticí speciálního typu
On a class of higher order methods for simultaneous rootfinding of generalized polynomials.
On a class of unsolvable operators
On a Companion Operator for Analytic Functions.
On a Computational Method for the Second Fundamental Tensor and its Application to Bifurcation Problems.
On a general convergence for Broyden like update method.
On a Global Descent Method for Polynomials.
On a Numerical Treatment for the Curve-Tracing of the Homotopy Method.
On acceleration methods for coupled nonlinear elliptic systems.
On alternative functional equations. (Short Communication).
On an estimation of the roots of algebraic equations
On Brown's method with convexity hypotheses
Given two initial points generating monotone convergent Brown iterations in the context of the monotone Newton theorem (MNT), it is proved that if one of them is an upper bound of the other, then the same holds for each pair of respective terms in the Brown sequences they generate. This comparison result is carried over to the corresponding Brown-Fourier iterations. An illustration is discussed.
On certain iterative sequences
On Condition Numbers and the Distance to the Nearest Ill-posed Problem.
On convergence of Börsch-Supan's method with Weierstrass' corrections.
On finding the largest root of a polynomial
On mesh independence and Newton-type methods
Mesh-independent convergence of Newton-type methods for the solution of nonlinear partial differential equations is discussed. First, under certain local smoothness assumptions, it is shown that by properly relating the mesh parameters and for a coarse and a fine discretization mesh, it suffices to compute the solution of the nonlinear equation on the coarse mesh and subsequently correct it once using the linearized (Newton) equation on the fine mesh. In this way the iteration error will be...
On multivariate Descartes' rule – a counterexample.
On Newton-like methods to enclose solutions of nonlinear equations
We present a class of Newton-like methods to enclose solutions of systems of nonlinear equations. Theorems are derived concerning the feasibility of the method, its global convergence, its speed and the quality of enclosure.
On Newton's Method.