Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The Jacobi matrix of the (2n+1)-point Gauss-Kronrod quadrature rule for a given measure is calculated efficiently by a five-term recurrence relation. The algorithm uses only rational operations and is therefore also useful for obtaining the Jacobi-Kronrod matrix analytically. The nodes and ights can then be computed directly by standard software for Gaussian quadrature formulas.
['Dirk P. Laurie']
I am writing a research paper on a idea Calculation of Gauss-Kronrod quadrature rules
[{"from": "human", "value": "I am writing a research paper on a idea Calculation of Gauss-Kronrod quadrature rules"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The Jacobi matrix of the (2n+1)-point Gauss-Kronrod quadrature rule for a given measure is calculated efficiently by a five-term recurrence relation. The algorithm uses only rational operations and is therefore also useful for obtaining the Jacobi-Kronrod matrix analytically. The nodes and ights can then be computed directly by standard software for Gaussian quadrature formulas."}]