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General orthogonal polynomials
Padé approximants and related matters
4 other sections not shown
algorithm applying approximant to f arbitrary BREZINSKI characteristic polynomial coefficients coeﬂicients compute recursively conjugate gradient method consecutive zeros construct continued fraction convergence Corollary cross rule deﬁned denominator denoted different from zero eigenvalues equal equations family of orthogonal ﬁnally ﬁnd ﬁnite ﬁrst ﬁxed value Gaussian quadrature Hankel determinants Hermite interpolation identical inﬁnite interpolation polynomial Lemma Let us assume linear mants Math matrix mials minimal polynomial monic Moreover Multiplying nondecreasing numerator obtain orthogonal polynomials orthogonal with respect orthogonality relations Padé approximants Padé table Padé-type approximants polyno polynomial of degree polynomial with degree polynomials Pk polynomials with respect positive deﬁnite preceding relation preceding results Proof proved rational approximation rational function recurrence relation result follows s-algorithm satisﬁed series f Shanks transformation term Theorem TM sequences topological variables vectors write written zeros of Pk