Displacement structure approach to q-adic Chebyshev–Vandermonde-like matrices |
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Authors: | Zhenghong Yang Cheng Li Zhengzhi Zhang |
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Institution: | aDepartment of Mathematics, College of Science, China Agricultural University, Beijing 100083, China;bStatistics Institute, Xi’an University of Finance and Economics, Xi’an 710100, China |
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Abstract: | In this paper, a new class of so-called q-adic Chebyshev–Vandermonde-like matrices over an arbitrary non-algebraically closed field is introduced. This class generalizes both the ordinary Chebyshev–Vandermonde-like matrices over the complex field studied earlier by Kailath and Olshevsky T. Kailath, V. Olshevsky, Displacement structure approach to Chebyshev–Vandermonde and related matrices, Integral Equations Operator Theory 22 (1995) 65–92], and the classical q-adic Vandermonde-like matrices with respect to power basis by Yang and Hu Z.H. Yang, Y.J. Hu, Displacement structure and fast inversion formulas for q-adic Vandermonde-like matrices, J. Comput. Appl. Math. 176 (2005) 1–14]. Three kinds of displacement structures and consequently, three kinds of fast inversion formulas are presented for this class of matrices by using displacement structure theory method, which generalize the corresponding results for Chebyshev–Vandermonde-like and q-adic Vandermonde-like matrices. |
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Keywords: | q-Adic Chebyshev– Vandermonde matrix Displacement structure Fast inversion formula |
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