A majorant principle for multipoint iterations without memory
A method for obtaining iterative formulas of higer order
A method for obtaining third-order iterative formulas.
A Modified Fast Fourier Transform for Polynomial Evaluation and the Jenkins-Traub Algorithm.
A new Variant of an Iterative Method for Solving the Complete Eigenvalue of Matrices
A Newton-Kantorovich-SOR type theorem
In this paper we propose a new method for solving nonlinear systems of equations in finite dimensional spaces, combining the Newton-Raphson's method with the SOR idea. For the proof we adapt Kantorovich's demonstration given for the Newton-Raphson's method. As applications we reobtain the classical Newton-Raphson's method and the author's Newton-Kantorovich-Seidel type result.
A note on Babylonian square-root algorithm and related variants.
A note on direct methods for approximations of sparse Hessian matrices
Necessity of computing large sparse Hessian matrices gave birth to many methods for their effective approximation by differences of gradients. We adopt the so-called direct methods for this problem that we faced when developing programs for nonlinear optimization. A new approach used in the frame of symmetric sequential coloring is described. Numerical results illustrate the differences between this method and the popular Powell-Toint method.
A note on Halley's method.
A note on Halley's method
A Note On M. Prešić's Method
A note on M. Presic's method.
A Note on the “Constructing” of Nonstationary Methods for Solving Nonlinear Equations with Raised Speed of Convergence
This paper is partially supported by project ISM-4 of Department for Scientific Research, “Paisii Hilendarski” University of Plovdiv.In this paper we give methodological survey of “contemporary methods” for solving the nonlinear equation f(x) = 0. The reason for this review is that many authors in present days rediscovered such classical methods. Here we develop one methodological schema for constructing nonstationary methods with a preliminary chosen speed of convergence.
A parallel projection method for linear algebraic systems
A direct projection method for solving systems of linear algebraic equations is described. The algorithm is equivalent to the algorithm for minimization of the corresponding quadratic function and can be generalized for the minimization of a strictly convex function.
A parametrized Newton method for nonsmooth equations with finitely many maximum functions
In this paper we propose a parametrized Newton method for nonsmooth equations with finitely many maximum functions. The convergence result of this method is proved and numerical experiments are listed.
A posteriori Error Bounds for the Zeros of a Polynomial.
A power series method for computing singular solutions to nonlinear analytic systems.
A projected Hessian Gauss-Newton algorithm for solving systems of nonlinear equations and inequalities.
A pseudo Laguerre method
A Rapid Generalized Method of Bisection for Solving Systems of Non-linear Equations.