Numerical stability of fast cosine transforms

• Published in: Numerical functional analysis and optimization Vol. 21; no. 1-2; pp. 25 - 46
• Main Authors: Baszenski, G., Schreiber, U., Tasche, G.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Philadelphia, PA Marcel Dekker, Inc 01.01.2000; Taylor & Francis
• Subjects: 65G05; Algebra; Error analysis; Exact sciences and technology; Fast cosine transform; fast Fourier transform; Fourier analysis; Linear and multilinear algebra, matrix theory; Mathematics; matrix factorization; Numerical analysis; Numerical analysis. Scientific computation; numerical stability; round off error analysis; Sciences and techniques of general use; worst case study; Permutation matrix; Fourier transformation; Error estimation; Fast Fourier transformation; Rounding error; Sparse matrix; Matrix factorization; Numerical stability; Cosine transform; Discrete cosine transform
• ISSN: 0163-0563; 1532-2467
• DOI: 10.1080/01630560008816938

In this paper we consider the numerical stability of fast algorithms for discrete cosine transform (DCT) of type III and II, respectively. We show that various fast DCTs can possess a very different behaviour of numerical stability. By matrix factorizations we find that a complex fast DCT which is based mainly on a fast Fouier transform has a better numerical stability than a real fast DCT despite its larger arithmetical complexity. Numerical tests illustrate our theoretical results.