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      Complex Jacobi Matrices and Gauss Quadrature for Quasi-definite Linear Functionals

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      linear functionals, jacobi matrix, quadrature, gauss quadrature, orthogonal polynomials, lanczos algorithm
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            Abstract

            The Gauss quadrature can be formulated as a method for approximation of positive definite linear functionals. The underlying theory connects several classical topics including orthogonal polynomials and (real) Jacobi matrices. In the poster we investigated the problem of generalizing the concept of Gauss quadrature for approximation of linear functionals which are not positive definite. We showed that the concept can be generalized to quasi-definite functionals and based on a close relationship with orthogonal polynomials and complex Jacobi matrices.

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