Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the third and fourth kinds

Article Mathematics, Applied

Averaged Gauss quadrature formulas: Properties and applications

Lothar Reichel et al.

Summary: The estimation of quadrature error in Gauss quadrature rules for approximating integrals is important in scientific computing. Anti-Gauss quadrature rules and averaged rules have been developed as improved approximations. Recent research has shown that these averaged rules can achieve higher accuracy than expected. This paper discusses methods to modify averaged rules to ensure their internal nodes.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2022)

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Article Mathematics, Applied

Internality of generalized averaged Gauss quadrature rules and truncated variants for modified Chebyshev measures of the first kind

Dusan Lj. Djukic et al.

Summary: The study investigates whether generalized averaged Gauss quadrature formulas for modified Chebyshev measures of the first kind are internal and can be effectively applied to estimate errors in associated Gauss quadrature rules.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS (2021)

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Article Mathematics, Applied

A new representation of generalized averaged Gauss quadrature rules

Lothar Reichel et al.

Summary: This paper presents a new representation of the generalized averaged Gauss formulas that offers an attractive alternative to the (2l + 1)-node Gauss-Kronrod rule, which may not exist with 2l + 1 real nodes. The representation is cheaper to evaluate than the available representation.

APPLIED NUMERICAL MATHEMATICS (2021)

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Article Mathematics, Applied