Fiedler-comrade and Fiedler-Chebyshev pencils
نویسندگان
چکیده
Fiedler pencils are a family of strong linearizations for polynomials expressed in the monomial basis, that include the classical Frobenius companion pencils as special cases. We generalize the definition of a Fiedler pencil from monomials to a larger class of orthogonal polynomial bases. In particular, we derive Fiedler-comrade pencils for two bases that are extremely important in practical applications: the Chebyshev polynomials of the first and second kind. The new approach allows one to construct linearizations having limited bandwidth: a Chebyshev analogue of the pentadiagonal Fiedler pencils in the monomial basis. Moreover, our theory allows for linearizations of square matrix polynomials expressed in the Chebyshev basis (and in other bases), regardless of whether the matrix polynomial is regular or singular, and for recovery formulae for eigenvectors, and minimal indices and bases.
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ورودعنوان ژورنال:
- SIAM J. Matrix Analysis Applications
دوره 37 شماره
صفحات -
تاریخ انتشار 2016