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Maroulas, John; Barnett, Stephen

Polynomials with respect to a general basis. I: Theory. (English) Zbl 0426.15011

J. Math. Anal. Appl. 72, 177-194 (1979).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0426.15011

Cited in 1 Review
Cited in 22 Documents

MSC:

15B57 Hermitian, skew-Hermitian, and related matrices
15A18 Eigenvalues, singular values, and eigenvectors

Keywords:

basis polynomial; power basis; Hessenberg matrix
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Full Text: DOI

References:

[1] Barnett, S., Matrices in Control Theory (1971), Van Nostrand-Reinhold: Van Nostrand-Reinhold London · Zbl 0245.93002
[2] Barnett, S., Matrices, polynomials and linear time—invariant systems, IEEE Trans. Automatic Control, 18, 1-10 (1973) · Zbl 0268.93016
[3] Barnett, S., A companion matrix analogue for orthogonal polynomials, Linear Algebra and Appl., 12, 197-208 (1975) · Zbl 0327.15026
[4] Datta, B. N.; Datta, K., An algorithm for computing powers of a Hessenberg matrix and its applications, Linear Algebra and Appl., 14, 273-284 (1976) · Zbl 0339.65018
[5] Good, I. J., The colleague matrix, a Chebyshev analogue of the companion matrix, Quart. J. Math. Oxford Ser., 12, 61-68 (1961) · Zbl 0103.01003
[6] Huang, C. P., Computing powers of arbitrary Hessenberg matrices, Linear Algebra and Appl., 21, 123-134 (1978) · Zbl 0396.15002
[7] Maroulas, J.; Barnett, S., Greatest common divisor of generalized polynomials and polynomial matrices, Linear Algebra and Appl., 22, 195-210 (1978) · Zbl 0392.15010
[8] Nomizou, K., Fundamentals of Linear Algebra (1966), MacGraw-Hill: MacGraw-Hill New York · Zbl 0148.01601
[9] Roychoudhury, D., Algorithm for power of companion matrix and its application, IEEE Trans. Automatic Control, 18, 173-180 (1973)
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