32 citations · 43 across the 12 of their papers we have counts for
10 papers · 1 filter
Numerical stability of the symplectic factorization
Maksymilian Bujok, Miroslav Rozložník, Agata Smoktunowicz +1
In this paper we give the detailed error analysis of two algorithms and for computing the symplectic factorization of a symmetric positive definite and symplectic matri…
On computing the symplectic factorization
Maksymilian Bujok, Alicja Smoktunowicz, Grzegorz Borowik
We analyze two algorithms for computing the symplectic factorization of a given symmetric positive definite symplectic matrix . The first algorithm is an i…
On constructing orthogonal generalized doubly stochastic matrices
Gianluca Oderda, Alicja Smoktunowicz, Ryszard Kozera
A real quadratic matrix is generalized doubly stochastic (g.d.s.) if all of its row sums and column sums equal one. We propose numerically stable methods for generating such matric…
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 the accuracy and stability of algorithms most commonly used in the evaluation of Chebyshev polynomials of the first kind
Alicja Smoktunowicz, Agata Smoktunowicz, Ewa Pawelec
This paper provides error analyses of the algorithms most commonly used for the evaluation of the Chebyshev polynomial of the first kind . Some of these algorithms are show…
Numerical solution of saddle point problems by block {Gram--Schmidt} orthogonalization
Felicja Okulicka-Dłużewska, Alicja Smoktunowicz
Saddle point problems arise in many important practical applications. In this paper we propose and analyze some algorithms for solving symmetric saddle point problems which are bas…
Reorthogonalized Block Classical Gram--Schmidt
Jesse L. Barlow, Alicja Smoktunowicz
A new reorthogonalized block classical Gram--Schmidt algorithm is proposed that factorizes a full column rank matrix into where is left orthogonal (has orthonormal c…
A note on the error analysis of classical Gram-Schmidt
Alicja Smoktunowicz, Jesse L. Barlow, Julien Langou
An error analysis result is given for classical Gram--Schmidt factorization of a full rank matrix into where is left orthogonal (has orthonormal columns) and is…
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…