5 papers
Numerical stability of iterative refinement with a relaxation for linear systems
Alicja Smoktunowicz, Jakub Kierzkowski, Iwona Wrobel
Stability analysis of Wilkinson's iterative refinement with a relaxation IR(omega) for solving linear systems is given. It extends existing results for omega=1, i.e., for Wilkinson…
On recursive algorithms for inverting tridiagonal matrices
Paweł Keller, Iwona Wróbel
If is a tridiagonal matrix, then the equations and defining the inverse of are in fact the second order recurrence relations for the elements in each row…
Roundoff errors in the problem of computing Cauchy principal value integrals
Paweł Keller, Iwona Wróbel
We investigate the possibility of fast, accurate and reliable computation of the Cauchy principal value integrals using st…
How to overcome the numerical instability of the scheme of divided differences?
Alicja Smoktunowicz, Przemyslaw Kosowski, Iwona Wrobel
The scheme of divided differences is widely used in many approximation and interpolation problems. Computing the Newton coefficients of the interpolating polynomial is the first st…
On improving the accuracy of Horner's and Goertzel's algorithms
Alicja Smoktunowicz, Iwona Wróbel
It is known that Goertzel's algorithm is much less numerically accurate than the Fast Fourier Transform (FFT)(Cf. \cite{gen:69}). In order to improve accuracy we propose modificati…