The concrete method of ‘surface spline interpolation’ is closely connected with the classical problem of minimizing a Sobolev seminorm under interpolatory constraints; the intrinsic structure of surface splines is a...
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The concrete method of ‘surface spline interpolation’ is closely connected with the classical problem of minimizing a Sobolev seminorm under interpolatory constraints; the intrinsic structure of surface splines is accordingly that of a multivariate extension of natural splines. The proper abstract setting is a Hilbert function space whose reproducing kernel involves no functions more complicated than logarithms and is easily coded. Convenient representation formulas are given, as also a practical multivariate extension of the Peano kernel theorem. Owing to the numerical stability of Cholesky factorization of positive definite symmetric matrices, the whole construction process of a surface spline can be described as a recursive algorithm, the data relative to the various interpolation points being exploited in sequence.
This paper presents a new recursive algorithm for computing bounds on the reliability of a directed, source-sink network whose arcs either function or fail with known probabilities. The reliability is the probability ...
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The Turing machine model is extended to allow for recursive calls and the basic theory of these machines is developed. The model is also used to study the following additional topics: The time and storage needed to im...
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The Turing machine model is extended to allow for recursive calls and the basic theory of these machines is developed. The model is also used to study the following additional topics: The time and storage needed to implement recursive algorithms by non-recursive algorithms, the storage needed to implement non-deterministic algorithms by deterministic algorithms, and the implementation of recursive algorithms by means of stack machines. Some attention is given to time bounds but the emphasis is on storage-bounded computations.
This paper considers the computation problems in feature selection. A recursive computation procedure is presented for feature selection and ordering by using the indirect measures such as the Bhattacharyya distance a...
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This paper considers the computation problems in feature selection. A recursive computation procedure is presented for feature selection and ordering by using the indirect measures such as the Bhattacharyya distance and mutual information. Both binary and quantized measurements are considered. Supporting computer results are provided.
The problem of pole assignment in linear, multivariable systems using an unconstrained-rank feedback matrix is considered. The effect of output feedback of unspecified rank on the characteristic polynomial of a multiv...
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The problem of pole assignment in linear, multivariable systems using an unconstrained-rank feedback matrix is considered. The effect of output feedback of unspecified rank on the characteristic polynomial of a multivariable system is first studied. The results are then used to derive a recursive algorithm for pole assignment without any restrictions on the rank of the output feedback matrix used. The method is based on the pseudoinverse concept for obtaining least-squares solutions of sets of linear equations, and is computationally efficient.
Recently, it has been discovered that symbolic algebraic manipulations can be performed on the computer with input/output data in symbolic form. Accordingly, and for slightly nonlinear two-point boundary-value problem...
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Recently, it has been discovered that symbolic algebraic manipulations can be performed on the computer with input/output data in symbolic form. Accordingly, and for slightly nonlinear two-point boundary-value problems, it is feasible to obtain approximate analytical solutions in the form of power series in a small parameter. In these solutions, the boundary values are presented in a literal form. In this paper, the Lie canonical transformation is applied to derive approximate optimal solutions for slightly nonlinear systems with quadratic criteria. The transformation generator is determined by simple partial differential equations of the first order. To determine the arbitrary constants of the transformation in terms of the two-point boundary values, inversion of a vectorial power series in a small parameter is required, and a recursive algorithm for this inversion is given. To express the final solution in terms of these boundary values, a substitution of the inverted vectorial power series into another vectorial power series is also necessary, and a recursive algorithm for this substitution is presented.
A method based on the matrix pseudoinverse is presented for the online identification of discrete-time systems of known order. recursive algorithms are described which provide minimum-norm estimates of the parameter v...
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A method based on the matrix pseudoinverse is presented for the online identification of discrete-time systems of known order. recursive algorithms are described which provide minimum-norm estimates of the parameter vector when insufficient data are available, and least-squares estimates with adequate data. These estimates can be updated easily with each pair of additional input-output data, as matrix inversion is not required. When the order of the system is not known, it may be determined offline using one of the two methods described. A recursive algorithm for calculating the residual error is also derived. A number of examples are given to illustrate the usefulness of the methods.
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