Error Estimates of Gaussian-type Quadratures—A Survey

Davorka R. Jandrlić (), Aleksandar V. Pejčev () and Miodrag M. Spalević ()
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Davorka R. Jandrlić: Department of Mathematics
Aleksandar V. Pejčev: Department of Mathematics
Miodrag M. Spalević: Department of Mathematics

Chapter Chapter 11 in Analysis, Approximation, Optimization: Computation and Applications, 2025, pp 195-209 from Springer

Abstract: Abstract This chapter offers a survey of our recent findings concerning error estimates in Gaussian-type quadrature formulas for analytic functions defined on confocal ellipses. Our recent research has focused on a methodology for numerically assessing error terms within Gaussian quadrature formulas, particularly examining a special case involving the Jacobi weight function ω ( t ) = ( 1 − t ) α ( 1 + t ) β $$\omega (t) = (1-t)^{\alpha }(1+t)^{\beta }$$ , α , β > −1 $$\alpha ,\beta >-1$$ . We initially addressed the scenario where both α $$\alpha $$ and β $$\beta $$ are zero, corresponding to the Legendre weight function. Subsequently, we expanded this investigation to encompass instances where α $$\alpha $$ and β $$\beta $$ represent any natural number, thereby relating to the Gegenbauer weight function.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-031-85743-0_11

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DOI: 10.1007/978-3-031-85743-0_11

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