Jacobi matrices
نویسنده
چکیده
We discuss the relationships among Jacobi matrices, orthogonal polynomials, spectral measure, moments, minors, Gaussian quadrature, resolvents and continued fractions in the simplest setting, namely the finite-dimensional one. The formal structure is essentially the same as that in the infinite-dimensional setting, where it leads into the rich analytic world of orthogonal polynomials on the real line. When the underlying measure is finitely supported, however, the analysis becomes trivial and the algebraic relationships are readily apparent.
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