Abstract
This Chapter is mainly devoted to formal orthogonal polynomials. These polynomials, which generalize the usual orthogonal polynomials, play a fundamental role in the algebraic theory of Padé approximants; see [13] and [14] for their introduction in this theory and [3] for an extended exposition of the subject. Formal orthogonal polynomials also form the basis of Lanczos methods for transforming a matrix into an equivalent tridiagonal one or for solving a system of linear algebraic equations. They are also involved in some convergence acceleration methods based on extrapolation. We will also study formal biorthogonal polynomials and their important particular case of vector orthogonal polynomials. Other notions of orthogonality are studied in [5].
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Brezinski, C. (2002). Formal Orthogonal Polynomials. In: Brezinski, C. (eds) Computational Aspects of Linear Control. Numerical Methods and Algorithms, vol 1. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0261-2_3
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DOI: https://doi.org/10.1007/978-1-4613-0261-2_3
Publisher Name: Springer, Boston, MA
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