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Infinite elementary divisor structure-preserving transformations for polynomial matrices

100%

Karampetakis N. P., Vologiannidis S.

International Journal of Applied Mathematics and Computer Science

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2003

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tom 13

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nr 4

493-503

EN

The main purpose of this work is to propose new notions of equivalence between polynomial matrices that preserve both the finite and infinite elementary divisor structures. The approach we use is twofold: (a) the 'homogeneous polynomial matrix approach', where in place of the polynomial matrices we study their homogeneous polynomial matrix forms and use 2-D equivalence transformations in order to preserve their elementary divisor structure, and (b) the 'polynomial matrix approach', where some conditions between the 1-D polynomial matrices and their transforming matrices are proposed.

2

Canonical forms of singular 1D and 2D linear systems

88%

Kaczorek T.

International Journal of Applied Mathematics and Computer Science

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2003

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tom 13

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nr 1

61-72

EN

The paper consists of two parts. In the first part, new canonical forms are defined for singular 1D linear systems and a procedure to determine nonsingular matrices transforming matrices of singular systems to their canonical forms is derived. In the second part new canonical forms of matrices of the singular 2D Roesser model are defined and a procedure for determining realisations in canonical forms for a given 2D transfer function is presented. Necessary and sufficient conditions for the existence of a pair of nonsingular block diagonal matrices transforming the matrices of the singular 2D Roesser model to their canonical forms are established. A procedure for computing the pair of nonsingular matrices is presented.

3

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Estimation of the hazard rate function with a reduction of bias and variance at the boundary

75%

Janiszewska B., Różański R.

Discussiones Mathematicae Probability and Statistics

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2005

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tom 25

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nr 1

5-37

EN

In the article, we propose a new estimator of the hazard rate function in the framework of the multiplicative point process intensity model. The technique combines the reflection method and the method of transformation. The new method eliminates the boundary effect for suitably selected transformations reducing the bias at the boundary and keeping the asymptotics of the variance. The transformation depends on a pre-estimate of the logarithmic derivative of the hazard function at the boundary.

Ograniczanie wyników

2 International Journal of Applied Mathematics and Computer Science

1 Discussiones Mathematicae Probability and Statistics

1 Janiszewska B.

1 Kaczorek T.

1 Karampetakis N. P.

1 Różański R.

1 Vologiannidis S.

1 2005

2 2003

Infinite elementary divisor structure-preserving transformations for polynomial matrices

Canonical forms of singular 1D and 2D linear systems

Estimation of the hazard rate function with a reduction of bias and variance at the boundary