Optimal Quadrature Formulas with Positive Coefficients in L₂^(m)(0,1) Space

2009/11/16 by Kh. M. Shadimetov, Shadimetov, Kh. M., A.R. Hayotov +1
Mathematics · #65D30 #65D32 #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #Numerical Analysis (math.NA) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.0911.2896

openalex publication_date 2009/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the Sobolev space L₂^(m)(0,1) optimal quadrature formulas with the nodes (1.5) are investigated. For optimal coefficients explicit form are obtained and norm of the error functional is calculated. In particular, by choosing parameter η₀ in (1.5) the optimal quadrature formulas with positive coefficients are obtained and compared with well known optimal formulas.

Related

• On an optimal quadrature formula in Sobolev space L₂^(m) (0,1)
• Optimal quadrature formulas of closed type in the space L₂^(m)(0,1)
• Calculation of Coefficients of the Optimal Quadrature Formulas in the W₂^m,m-1(0,1) Space
• Optimal quadrature formulas with derivatives in Sobolev space
• Optimal Quadrature Formulas in the Sense of Sard in W₂^(m,m-1) Space