Università di Pisa
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Gemignani, Luca (1996) MANIPULATING POLYNOMIALS IN GENERALIZED FORM. Technical Report del Dipartimento di Informatica . Università di Pisa, Pisa, IT.

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    We present new algorithms using structured matrix methods for manipulating polynomials expressed in generalized form, that is, relative to a polynomial basis $\{p_i(x)\}$ satisfying a three-term recurrence relation. This includes computing the Euclidean remainders as well as the greatest common divisor of two polynomials $u(x)$ and $v(x)$ of degrees less than $n$. The computational schemes involve solving linear systems with nested Hankel matrices represented in the given generalized basis and they reach the optimal sequential complexity of $O(n^2)$ arithmetical operations.

    Item Type: Book
    Uncontrolled Keywords:
    Subjects: Area01 - Scienze matematiche e informatiche > INF/01 - Informatica
    Divisions: Dipartimenti (until 2012) > DIPARTIMENTO DI INFORMATICA
    Depositing User: dott.ssa Sandra Faita
    Date Deposited: 23 Jan 2015 11:11
    Last Modified: 23 Jan 2015 11:11
    URI: http://eprints.adm.unipi.it/id/eprint/1968

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