Numerical integration as a finite matrix approximation to multiplication operator

@article{Sarmavuori2017NumericalIA,
  title={Numerical integration as a finite matrix approximation to multiplication operator},
  author={Juha Sarmavuori and Simo S{\"a}rkk{\"a}},
  journal={ArXiv},
  year={2017},
  volume={abs/1912.07325}
}
View PDF on arXiv
3 Citations
Background Citations
1

Figures and Tables from this paper

3 Citations

Strong Resolvent Convergence of Finite Matrix Approximations in Numerical Integration.

We study the convergence of a family of numerical integration methods where the numerical integration is formulated as a finite matrix approximation to a multiplication operator. For bounded…

New Formulas of Numerical Quadrature Using Spline Interpolation

This work develops formulas for numerical integration with spline interpolation. The new formulas are shown to be alternatives to the Newton–Cotes integration formulas. These methods have important…

New Formulas of Numerical Quadrature Using Spline Interpolation

This work develops formulas for numerical integration with spline interpolation. The new formulas are shown to be alternatives to the Newton–Cotes integration formulas. These methods have important…

References

SHOWING 1-10 OF 80 REFERENCES

Spectra of Multiplication Operators as a Numerical Tool

A numerical procedure for the construction of interpolation and quadrature formulae on bounded convex regions in the plane based on the behavior of spectra of certain multiplication operators and leads to nodes which are inside a prescribed convex region in R2.

Spectral Approximation of Multiplication Operators

A linear operator on a Hilbert space may be approximated with finite matrices by choosing an orthonormal basis of the Hilbert space. For an operator that is not compact such approximations cannot…

Generalized Gaussian quadrature rules for systems of arbitrary functions

A numerical algorithm is presented for the construction of generalized Gaussian quadrature rules, originally introduced by S. Karlin and W. Studden over three decades ago. The quadrature rules to be…

Finite-dimensional approximations of the resolvent of an infinite band matrix and continued fractions

The approximability of the resolvent of an operator induced by a band matrix by the resolvents of its finite-dimensional sections is studied. For bounded perturbations of self-adjoint matrices a…

A matrix approach to the computation of quadrature formulas on the unit circle

On the approximation of spectra of linear operators on Hilbert spaces

A matricial computation of rational quadrature formulas on the unit circle

A matricial computation of quadrature formulas for orthogonal rational functions on the unit circle, is presented in this paper and it is shown how these nodes can be obtained as the eigenvalues of the operator Möbius transformations of Hessenberg matrices and also as the Eigenvalue of the operators of five-diagonal matrices recently obtained.

Linear Operators in Hilbert Spaces

Motivated by the eigenvalue problems for ordinary and partial differential operators, we shall develop the spectral theory for linear operators in Hilbert spaces. Here we transform the unbounded…

Orthogonal polynomials: applications and computation

  • W. Gautschi
  • Mathematics, Computer Science
    Acta Numerica
  • 1996
Numerical methods applicable to computing Gauss-type quadrature rules and Sobolev orthogonal polynomials, although their recurrence relations are more complicated are discussed.

Matrix methods for quadrature formulas on the unit circle. A survey

...