Approximate integration formulas for certain spherically symmetric regions

Stroud, A. H.; Secrest, Don

doi:10.1090/s0025-5718-1963-0161473-0

Cited by 46 publications

(15 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the case of integration over an infinitely extended region with weight function exp [-"52 x¿2] (see Stroud and Secrest [5] or Lyness [4]), we find fc = i 4. A Lower Bound on F(S((ii).…”

Section: Sets and Classes Of Basicmentioning

confidence: 86%

Limits on the number of function evaluations required by certain high-dimensional integration rules of hypercubic symmetry

Lyness¹

1965

Math. Comp.

View full text Add to dashboard Cite

show abstract

“…In the case of integration over an infinitely extended region with weight function exp [-"52 x¿2] (see Stroud and Secrest [5] or Lyness [4]), we find fc = i 4. A Lower Bound on F(S((ii).…”

Section: Sets and Classes Of Basicmentioning

confidence: 86%

Limits on the number of function evaluations required by certain high-dimensional integration rules of hypercubic symmetry

Lyness¹

1965

Math. Comp.

View full text Add to dashboard Cite

show abstract

“…The fact that the expectations are taken with respect to a member of an exponential family can be exploited for efficient numerical computation. For example, if is a Gaussian distribution, efficient quadrature rules are known, where for state vectors of dimension , only or point-wise evaluations are needed to obtain cubature formulae of degree 3 or 5, respectively [27], [44].…”

Section: Remarkmentioning

confidence: 99%

Belief Condensation Filtering

Mazuelas

Shen

Win

2013

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

Abstract-Inferring a sequence of variables from observations is prevalent in a multitude of applications. Traditional techniques such as Kalman filters (KFs) and particle filters (PFs) are widely used for such inference problems. However, these techniques fail to provide satisfactory performance in many important nonlinear or non-Gaussian scenarios. In addition, there is a lack of a unified methodology for the design and analysis of different filtering techniques. To address these problems, in this paper, we propose a new filtering methodology called belief condensation (BC) filtering. First, we establish a general framework for filtering techniques and propose an optimality criterion that leads to BC filtering. We then propose efficient BC algorithms that can best represent the complex distributions arising in the filtering process. The performance of the proposed techniques is evaluated for two representative nonlinear/non-Gaussian problems, showing that the BC filtering can provide accuracy approaching the theoretical bounds and outperform existing techniques in terms of the accuracy versus complexity tradeoff.

show abstract

“…In such applications one can again resort to non-product monomial rules. Stroud and Secrest (1963) derive the following two rules (covered also in chapter 7 of Judd, 1998):…”

Section: Rules For the N-dimensional Space With Weight Function E −Xmentioning

confidence: 99%

Solving the multi-country Real Business Cycle model using a monomial rule Galerkin method

Pichler¹

2011

Journal of Economic Dynamics and Control

View full text Add to dashboard Cite

I propose a Galerkin projection method for solving dynamic economic models with many state variables. This method employs non-product monomial integration formulas for the computation of weighted residuals, and its computational cost therefore increases only polynomially in the model's dimensionality. I illustrate the practical implementation of the proposed algorithm by solving several specifications of the multi-country Real Business Cycle model described in Den Haan et al.

show abstract

Approximate integration formulas for certain spherically symmetric regions

Cited by 46 publications

References 9 publications

Limits on the number of function evaluations required by certain high-dimensional integration rules of hypercubic symmetry

Limits on the number of function evaluations required by certain high-dimensional integration rules of hypercubic symmetry

Belief Condensation Filtering

Solving the multi-country Real Business Cycle model using a monomial rule Galerkin method

Contact Info

Product

Resources

About