11,177 research outputs found

    Higher-order iterative methods for approximating zeros of analytic functions

    Get PDF
    AbstractIterative methods with extremely rapid convergence in floating-point arithmetic and circular arithmetic for simultaneously approximating simple zeros of analytic functions (inside a simple smooth closed contour in the complex plane) are presented. The R-order of convergence of the basic total-step and single-step methods, as well as their improvements which use Newton's and Halley's corrections, is given. Some hybrid algorithms that combine the efficiency of ordinary floating-point iterative methods with the accuracy control provided by interval arithmetic are also considered

    A family of root-finding methods with accelerated convergence

    Get PDF
    AbstractA parametric family of iterative methods for the simultaneous determination of simple complex zeros of a polynomial is considered. The convergence of the basic method of the fourth order is accelerated using Newton's and Halley's corrections thus generating total-step methods of orders five and six. Further improvements are obtained by applying the Gauss-Seidel approach. Accelerated convergence of all proposed methods is attained at the cost of a negligible number of additional operations. Detailed convergence analysis and two numerical examples are given

    Laguerre-like methods for the simultaneous approximation of polynomial multiple zeros

    Get PDF
    Two new methods of the fourth order for the simultaneous determination of multiple zeros of a polynomial are proposed. The presented methods are based on the fixed point relation of Laguerre's type and realized in ordinary complex arithmetic as well as circular complex interval arithmetic. The derived iterative formulas are suitable for the construction of modified methods with improved convergence rate with negligible additional operations. Very fast convergence of the considered methods is illustrated by two numerical examples

    Summary of the functions and capabilities of the structural analysis system computer program

    Get PDF
    Functions and operations of structural analysis system computer progra

    Propagation of charged particle waves in a uniform magnetic field

    Full text link
    This paper considers the probability density and current distributions generated by a point-like, isotropic source of monoenergetic charges embedded into a uniform magnetic field environment. Electron sources of this kind have been realized in recent photodetachment microscopy experiments. Unlike the total photocurrent cross section, which is largely understood, the spatial profiles of charge and current emitted by the source display an unexpected hierarchy of complex patterns, even though the distributions, apart from scaling, depend only on a single physical parameter. We examine the electron dynamics both by solving the quantum problem, i. e., finding the energy Green function, and from a semiclassical perspective based on the simple cyclotron orbits followed by the electron. Simulations suggest that the semiclassical method, which involves here interference between an infinite set of paths, faithfully reproduces the features observed in the quantum solution, even in extreme circumstances, and lends itself to an interpretation of some (though not all) of the rich structure exhibited in this simple problem.Comment: 39 pages, 16 figure
    • ā€¦
    corecore