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This work reports on a new software for solving linear systems
involving affine-linear dependencies between complex-valued interval parameters.
We discuss the implementation of a parametric residual iteration
for linear interval systems by advanced communication between the system
Mathematica and the library C-XSC supporting rigorous complex interval
arithmetic. An example of AC electrical circuit illustrates the use of the
presented software.* This work was partly supported by the DFG grant GZ:...
In this paper we investigate the behavior of the discrete time AR (Auto Regressive) representations over a finite time interval, in terms of the finite and infinite spectral structure of the polynomial matrix involved in the AR-equation. A boundary mapping equation and a closed formula for the determination of the solution, in terms of the boundary conditions, are also gived.
Discrete wavelets are viewed as linear algebraic transforms given by banded orthogonal matrices which can be built up from small matrix blocks satisfying certain conditions. A generalization of the finite support Daubechies wavelets is discussed and some special cases promising more rapid signal reduction are derived.
The paper is devoted to an algorithm for computing matrices and for a given square matrix and a real . The algorithm uses the binary expansion of and has the logarithmic computational complexity with respect to . The problem stems from the control theory.
The paper introduces the calculation of a greatest common divisor of two univariate polynomials. Euclid’s algorithm can be easily simulated by the reduction of the Sylvester matrix to an upper triangular form. This is performed by using - transformation and -factorization methods. Both procedures are described and numerically compared. Computations are performed in the floating point environment.
We give a short introduction to a method for the data-sparse approximation of matrices resulting from the discretisation of non-local operators occurring in boundary integral methods or as the inverses of partial differential operators. The result of the approximation will be the so-called hierarchical matrices (or short -matrices). These matrices form a subset of the set of all matrices and have a data-sparse representation. The essential operations for these matrices (matrix-vector and matrix-matrix...
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