Результаты поиска по 'effective rank':
Найдено статей: 2
  1. Chulichkov A.I., Yuan B.
    Effective rank of a problem of function estimation based on measurement with an error of finite number of its linear functionals
    Computer Research and Modeling, 2014, v. 6, no. 2, pp. 189-202

    The problem of restoration of an element f of Euclidean functional space  L2(X) based on the results of measurements of a finite set of its linear functionals, distorted by (random) error is solved. A priori data aren't assumed. Family of linear subspaces of the maximum (effective) dimension for which the projections of element f to them allow estimates with a given accuracy, is received. The effective rank ρ(δ) of the estimation problem is defined as the function equal to the maximum dimension of an orthogonal component Pf of the element f which can be estimated with a error, which is not surpassed the value δ. The example of restoration of a spectrum of radiation based on a finite set of experimental data is given.

    Keywords: mathematical model of measurement, measurement reduction, spectrometry, optimum decisions, singular decomposition, effective rank.
  2. Sviridenko A.B., Zelenkov G.A.
    Correlation and realization of quasi-Newton methods of absolute optimization
    Computer Research and Modeling, 2016, v. 8, no. 1, pp. 55-78

    Newton and quasi-Newton methods of absolute optimization based on Cholesky factorization with adaptive step and finite difference approximation of the first and the second derivatives. In order to raise effectiveness of the quasi-Newton methods a modified version of Cholesky decomposition of quasi-Newton matrix is suggested. It solves the problem of step scaling while descending, allows approximation by non-quadratic functions, and integration with confidential neighborhood method. An approach to raise Newton methods effectiveness with finite difference approximation of the first and second derivatives is offered. The results of numerical research of algorithm effectiveness are shown.

    Keywords: Newton methods, quasi-Newton methods, Cholesky factorization, step scaling, method of confidence neighborhoods, finite difference approximation, algorithm, numerical research, absolute optimization.
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