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Proprieta' delle matrici tridiagonali ad elementi ed a blocchi. Monografia dell'Istituto di Elaborazione dell'Informazione del CNR
No full text
Fast parallel and sequential computations and spectral properties concerning band Toeplitz matrices
No full textSPECTRAL AND COMPUTATIONAL PROPERTIES OF BAND SYMMETRIC TOEPLITZ MATRICES
No full textAbstractWe are investigating spectral properties of band symmetric Toeplitz matrices (BST matrices). By giving a suitable representation of a BST matrix, we achieve separation results and multiplicity conditions for the eigenvalues of a 7°r 5-diagonal BST matrix and also structural properties of the eigenvectors. We give eigenvalue bounds for a 2k 1-diagonal BST matrix and also necessary and sufficient conditions for positive definiteness which are easy to check. The same conditions apply in the case of block BST matrices, either with full blocks or with BST blocks. We exhibit fast computational methods for the evaluation of the determinant and the characteristic polynomial of a BST matrix, either for sequential or for parallel computations. Two algorithms, based on the bisection technique and Newton's method, are shown to be very fast for computing the eigenvalues of a 7− or 5-diagonal BST-matrix
A CLASS OF CUBIC-SPLINES OBTAINED THROUGH MINIMUM CONDITIONS
No full textA class of cubic spline minimizing some special functional is investigated. This class is determined by the solution of a quadratic programming problem in which the minimizing function depends linearly on a parameter
α
>
2
\alpha > 2
. For
α
=
1
/
2
\alpha = 1/2
natural splines are obtained. For
α
=
−
1
\alpha = - 1
the spline minimizing the mean value of the third derivative is obtained. It is shown that this spline has the best convergence order.</p
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