K. Šalkauskas
Abstract
The condition that an interpolatory quadrature formula on n nodes have degree of precision at least n and positive weights defines a homeomorphism between the sets of admissible nodes and weights of such formulae for each n . This is used to prove that the only formulae having "almost equal" weights are the Chebyshev formulae.
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The condition that an interpolatory quadrature formula on n nodes have degree of precision at least n and positive weights defines a homeomorphism between the sets of admissible nodes and weights of such formulae for each n . This is used to prove that the only formulae having "almost equal" weights are the Chebyshev formulae.
Key concepts: Mathematics, Quadrature (astronomy), Chebyshev filter, Combinatorics, Mathematical analysis, Engineering, Electrical engineering