Gauss quadratures and Jacobi matrices for weight functions not of one sign

Gauss Quadratures and Jacobi Matrices for Weight Functions Not of One Sign

Construction of Gauss quadratures with prescribed knots via Jacobi matrices is extended to the case where not all orthogonal polynomials exist due to the weight function changing sign. An algorithm is described and is demonstrated by calculating the knots of Kronrod schemes and other Gauss quadratures with prescribed knots.

Generalized Gauss-Radau and Gauss-Lobatto formulas with Jacobi weight functions

We derive explicitly the weights and the nodes of the generalized Gauss-Radau and Gauss-Lobatto quadratures with Jacobi weight functions. AMS subject classification: 65D32, 65D30, 41A55.

Two modified Jacobi methods for M-matrices

Exponential convergence of Gauss-Jacobi quadratures for singular integrals over high dimensional simplices

Galerkin discretizations of integral operators in R d require the evaluation of integrals R S (1) R S (2) f (x, y) dydx where S (1) , S (2) are d-dimensional simplices and f has a singularity at x = y. In [3] we constructed a family of hp-quadrature rules Q N with N function evaluations for a class of integrands f allowing for algebraic singularities at x = y, possibly non-integrable with respe...

Exponential Convergence of Gauss-Jacobi Quadratures for Singular Integrals over Simplices in Arbitrary Dimension

It is advisable to refer to the publisher's version if you intend to cite from the work. Abstract. Galerkin discretizations of integral operators in R d require the evaluation of integrals S (1) S (2) f (x, y) dydx,w h e r eS (1) ,S (2) are d-dimensional simplices and f has a singularity at x = y. In [A. Chernov, T. von Petersdorff, and C. Schwab, M2A NM a t h .M o d e l .N u m e r .A n a l. , ...