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- W1762106914 abstract "Any quadrature formula with positive coefficients induces a discrete inner product with respect to which orthogonal polynomials may be defined. The discrete linear functionals that evaluate the coefficients in the expansion of a function in terms of these polynomials are null rules, i.e. they map polynomials of sufficiently low degree to zero. Moreover, they are orthogonal to one another and to the quadrature rule itself with respect to the dual inner product.It is suggested that this way of obtaining null rules is preferable to the current method of using null rules that are orthogonal to one another in the Euclidean sense, but not to the quadrature rule. One advantage of the orthogonal expansion approach is that polynomial approximants can explicitly be constructed, leading to non-linear null rules that behave less capriciously than linear ones." @default.
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- W1762106914 date "1994-01-01" @default.
- W1762106914 modified "2023-10-04" @default.
- W1762106914 title "Null Rules and Orthogonal Expansions" @default.
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- W1762106914 doi "https://doi.org/10.1007/978-1-4684-7415-2_23" @default.
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