On orthogonal collocation by the zeros of orthogonal 0-interpolants
نویسندگان
چکیده
منابع مشابه
ORTHOGONAL ZERO INTERPOLANTS AND APPLICATIONS
Orthogonal zero interpolants (OZI) are polynomials which interpolate the “zero-function” at a finite number of pre-assigned nodes and satisfy orthogonality condition. OZI’s can be constructed by the 3-term recurrence relation. These interpolants are found useful in the solution of constrained approximation problems and in the structure of Gauss-type quadrature rules. We present some theoretical...
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متن کاملorthogonal zero interpolants and applications
orthogonal zero interpolants (ozi) are polynomials which interpolate the “zero-function” at a finite number of pre-assigned nodes and satisfy orthogonality condition. ozi’s can be constructed by the 3-term recurrence relation. these interpolants are found useful in the solution of constrained approximation problems and in the structure of gauss-type quadrature rules. we present some theoretical...
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Let a1 < a2 < . . . < a2l, Ej = [a2j−1, a2j ], put E = ⋃l j=1 Ej and H(x) = ∏2l j=1(x − aj). Furthermore let pn(x) = x + . . . be the polynomial of degree n orthogonal on E with respect to a weight function of the form w/ √ −H with square root singularities at the boundary points of E and w ∈ C(E). We study and answer the following questions: how many zeros has pn in the interval Ej , j ∈ {1, ....
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Let x1 and xk be the least and the largest zeros of the Laguerre or Jacobi polynomial of degree k. We shall establish sharp inequalities of the form x1 < A, xk > B, which are uniform in all the parameters involved. Together with inequalities in the opposite direction, recently obtained by the author, this locates the extreme zeros of classical orthogonal polynomials with the relative precision,...
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ژورنال
عنوان ژورنال: PAMM
سال: 2007
ISSN: 1617-7061,1617-7061
DOI: 10.1002/pamm.200700874