A superfast solver for real symmetric Toeplitz systems using real trigonometric transformations | Zendy

Codevico G. | Zendy; Heinig G. | Zendy; Van Barel M. | Zendy

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A superfast solver for real symmetric Toeplitz systems using real trigonometric transformations

Author(s) -

Codevico G.,

Heinig G.,

Van Barel M.

Publication year - 2005

Publication title -

numerical linear algebra with applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.02

H-Index - 53

eISSN - 1099-1506

pISSN - 1070-5325

DOI - 10.1002/nla.445

Subject(s) - toeplitz matrix , mathematics , solver , trigonometric interpolation , trigonometry , interpolation (computer graphics) , chebyshev polynomials , interpretation (philosophy) , trigonometric polynomial , inversion (geology) , polynomial , algorithm , polynomial interpolation , algebra over a field , mathematical analysis , pure mathematics , linear interpolation , mathematical optimization , computer science , animation , paleontology , computer graphics (images) , structural basin , biology , programming language

A new superfast O ( n log 2 n ) complexity direct solver for real symmetric Toeplitz systems is presented. The algorithm is based on 1. the reduction to symmetric right‐hand sides, 2. a polynomial interpretation in terms of Chebyshev polynomials, 3. an inversion formula involving real trigonometric transformations and 4. an interpretation of the equations as a tangential interpolation problem. The tangential interpolation problem is solved via a divide and conquer strategy and fast DCT. Copyright © 2005 John Wiley & Sons, Ltd.

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