Contribution to Book
Fast and Stable Algorithms for Discrete Sine Transformations having Orthogonal Factors
Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science
(2015)
Abstract
In this chapter we derive fast, recursive, and numerically stable radix-2 algorithms for discrete sine transformations (DST) having sparse and orthogonal factors. These real radix-2 stable algorithms are completely recursive, fast, and based on the simple orthogonal factors. Comparing to the known bulky and mostly unstable DST algorithms, our algorithms are easy to implement and use only permutations, scaling by constants,butterfly operations, and plane rotations/rotation-reflections.
For a given vector x, we also analyze error bounds of computing for the y = S x for the presented DST algorithms: S. Finally a classification of these real radix-2 DST algorithms enables us to establish the excellent forward and backward stability based on the sparse and orthogonal factors.
Keywords
- Discrete Fourier Transform,
- Error Bound,
- Recursive Algorithm
Disciplines
Publication Date
2015
Editor
M. Cojocaru, I. S. Kotsireas, R. Makarov, R. Melnik, and H. Shodiev
Publisher
Springer
DOI
10.1007/978-3-319-12307-3_50
Citation Information
Sirani M. Perera and Vadim Olshevsky, Fast and Stable Algorithms for Discrete Sine Transformations having Orthogonal Factors, In: M. Cojocaru, I. S. Kotsireas, R. Makarov, R. Melnik, and H. Shodiev (Eds.): Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science, vol. 117: 347-354, Springer, (2015)-DOI 10.1007/978-3-319-12307-3_50