Padé-Type Approximation and General Orthogonal Polynomials |
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A₁ Ak+1 Ak+1hk algorithm applying arbitrary B₁ BEGIN AGAIN EVERYTHING Bk+1 BREZINSKI c₁ characteristic polynomial Christoffel-Darboux relation Ck+1 Cn+1 coefficients conjugate gradient method consecutive zeros continued fraction convergence Corollary defined denominator denoted dk+1 e-algorithm eigenvalues equations formula Gaussian quadrature Hankel determinants Hermite interpolation Hk Co identical interpolation polynomial k₁ k₂ Lemma Let us assume linear Math matrix method monic Moreover Multiplying n+k/k necessary and sufficient numerator obtain orthogonal polynomials orthogonal with respect orthogonality relations P₁ Padé approximants Padé table Padé-type approximants Pk+1 polyno polynomial of degree polynomials Q positive definite power series preceding relation Proof proved quadrature rational function recurrence relation result follows S₁ satisfied Sk+1 sufficient condition Theorem TM sequences v₁ vectors WANT TO COMPUTE write Wynn x₁ Ž Ž z₁ zeros of Pk Σ Σ Сп