# A Survey of Gauss-Christoffel Quadrature Formulae

@inproceedings{Gautschi1981ASO, title={A Survey of Gauss-Christoffel Quadrature Formulae}, author={Walter Gautschi}, year={1981} }

We present a historical survey of Gauss-Christoffel quadrature formulae, beginning with Gauss’ discovery of his well-known method of approximate integration and the early contributions of Jacobi and Christoffel, but emphasizing the more recent advances made after the emergence of powerful digital computing machinery. One group of inquiry concerns the development of the quadrature formula itself, e.g. the inclusion of preassigned nodes and the admission of multiple nodes, as well as other…

## 221 Citations

### Accurate Computation of Weights in Classical Gauss-Christoffel Quadrature Rules

- Computer Science
- 1996

A simple but efficient and general method for improving the accuracy of the computation of the quadrature weights is proposed, which ensures a high level of accuracy for these weights even though the nodes may carry a significant large error.

### On sensitivity of Gauss–Christoffel quadrature

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- 2007

It is shown that even a small perturbation of a distribution function can cause large differences in Gauss–Christoffel quadrature estimates.

### Is Gauss Quadrature Better than Clenshaw-Curtis?

- Computer ScienceSIAM Rev.
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### Stieltjes Polynomials and the Error of Gauss-Kronrod Quadrature Formulas

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- 1999

The Gauss-Kronrod quadrature scheme, which is based on the zeros of Legendre polynomials and Stieltjes polynomials, is the standard method for automatic numerical integration in mathematical software…

### Anti-Gaussian quadrature formulae based on the zeros of Stieltjes polynomials

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- 2018

It is well known that the Gauss–Kronrod quadrature formula does not always exist with real and distinct nodes and positive weights. In 1996, in an attempt to find an alternative to the Gauss–Kronrod…

### Quadrature Rules with Multiple Nodes

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- 2016

In this paper a brief historical survey of the development of quadrature rules with multiple nodes and the maximal algebraic degree of exactness is given. The natural generalization of such rules are…

### Quadrature formulae of non-standard type

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- 2005

We discuss quadrature formulae of highest algebraic degree of precision for integration of functions of one or many variables which are based on non-standard data, i.e., in which the information used…

### The Australian Journal of Mathematical Analysis and Applications

- Mathematics, Computer Science
- 2004

This paper presents a fast algorithm for computing Gaussian type quadrature formulae which are exact for splinefunctions and which contain boundary terms involving derivatives at both end points and shows that the latter are computed, via eigenvalues and eigenvectors of real symmetric tridiagonal matrices.

### Gauss-Kronrod integration rules for Cauchy principal value integrals

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- 1983

Kronrod extensions to two classes of Gauss and Lobatto integration rules for the evaluation of Cauchy principal value integrals are derived. Since in one frequently occurring case, the Kronrod…

### Gene H. Golub and Gérard Meurant: Matrices, Moments and Quadrature with Applications

- MathematicsFound. Comput. Math.
- 2011

In modern computational mathematics, sciences and engineering, Krylov subspace methods and matching moments model reduction can be viewed as nothing but a translation of the classical concepts mentioned above to the language of large-scale matrix computation.

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