# Journal of Computational and Applied Mathematics

Journal of Computational and Applied Mathematics > 1995 > 57 > 1-2 > 251-260

Journal of Computational and Applied Mathematics > 1995 > 57 > 1-2 > 3-15

_{k}) such thatr

_{k}= b - Ax

_{k}=P

_{k}(A)r

_{0}, where P

_{k}is the orthogonal polynomial of degree at most k with respect to the linear functionalc whose moments are c(ζ

^{i}) = (y, A

^{i}r

_{0}). LetP

^{(}

^{1}

^{)}

_{k}be the regular monic polynomial...

Journal of Computational and Applied Mathematics > 1995 > 57 > 1-2 > 77-86

_{n}} be a sequence in the unit disk D = {z C: z < 1} consisting of a finite number of points cyclically repeated, and let L be the linear space generated by the functions B

_{n}(z) =

^{n}

_{k}

_{=}

_{0}- α

_{k}(z - α

_{k})

_{k}(1 -

_{k}z). Let {

_{n}(z)} be orthogonal rational functions obtained from the sequence {B ...

Journal of Computational and Applied Mathematics > 1995 > 57 > 1-2 > 135-146

_{n}and their respective remainder terms R

_{n}of algebraic degree deg(R

_{n}) = m being defined in (1.1)-(1.3) below. By comparison with Gaussian formulas and with help of inequalities for Legendre polynomials, we prove new inequalities for the variance Var(Q

_{n}) of quadrature formulasQ

_{n}. In particular, for interpolatory...

Journal of Computational and Applied Mathematics > 1995 > 57 > 1-2 > 123-133

_{q}(su(1, 1)) as example, we shall show that its metaplectic representation provides a group-theoretic setting for certain basic orthogonal polynomials...

Journal of Computational and Applied Mathematics > 1995 > 57 > 1-2 > 147-162

Journal of Computational and Applied Mathematics > 1995 > 57 > 1-2 > 163-170

_{n}(x)}

^{∞}

_{n}

_{=}

_{0}be a system of polynomials satisfying the recurrence relationP

_{-}

_{1}(x) = 0, P

_{0}(x) = 1, P

_{n}

_{+}

_{1}(x) + h

_{n}P

_{n}

_{-}

_{1}(x) + c

_{n}P

_{n}(x) = xP

_{n}(x)h

_{n}, c

_{n}are real sequences and h

_{n}> 0,n = 0, 1, 2, . The co-recursive...

Journal of Computational and Applied Mathematics > 1995 > 57 > 1-2 > 203-213

Journal of Computational and Applied Mathematics > 1995 > 57 > 1-2 > 271-281

Journal of Computational and Applied Mathematics > 1995 > 57 > 1-2 > 239-249

_{n}(x))

^{∞}

_{n}

_{=}

_{0}, is called a semiclassical OPS.In this...

Journal of Computational and Applied Mathematics > 1995 > 57 > 1-2 > 17-27

_{R}f(x) g(x) dψ(x) + λΔf(c) Δg(c),c R and ψ is a distribution function with infinite spectrum such that ψ has no points of increase in the interval (c, c + 1). Furthermore λ 0, f and g are functions on R and Δf(c) =f (c + 1) - f(c).Let {Q

^{λ}

_{n}(x)} be the sequence of monic orthogonal polynomials with respect to this inner...

Journal of Computational and Applied Mathematics > 1995 > 57 > 1-2 > 181-192

_{n}) be the sequence given by the Jacobi-Gauss quadrature method when the integrand is an analytic function with different kinds of poles located outside the interval of integration, and S its limit. We give an asymptotic representation of the errors S -- S

_{n}and of S

_{n}

_{+}

_{1}-- S

_{n}, which leads to build other sequences which give a better approximation...

Journal of Computational and Applied Mathematics > 1995 > 57 > 1-2 > 171-180

_{n}(w) the minimal number of nodes for which a Chebyshev-type formula for the weight function w exists having degree of exactnessn . The asymptotic behavior of N

_{n}(w) is determined for Jacobi weight functions with nonnegative parameters. Also some numerical results are given.

Journal of Computational and Applied Mathematics > 1995 > 57 > 1-2 > 261-269

Journal of Computational and Applied Mathematics > 1995 > 57 > 1-2 > 293-307

Journal of Computational and Applied Mathematics > 1995 > 57 > 1-2 > 215-237

Journal of Computational and Applied Mathematics > 1995 > 57 > 1-2 > 193-202

^{k}, accelerate the convergence of the partial sums Σ ...

Journal of Computational and Applied Mathematics > 1995 > 57 > 1-2 > 87-97

_{q}(2)...

Journal of Computational and Applied Mathematics > 1995 > 57 > 1-2 > 283-291

Journal of Computational and Applied Mathematics > 1995 > 57 > 1-2 > 57-76

_{n}of rational functions of degree n at most with given poles 1/

_{i}, α

_{i}< 1,i = 1 n. Let L =

^{∞}

_{0}L

_{n}. Given a finite positive measure μ on the unit circle, we associate with it an inner product onL by f, g = ∫ fgdμ. Suppose k

_{n}(z, w) is the reproducing kernel for L

_{n}, i.e., f(z),...