Einführung in die Numerische Mathematik I

Stoer, Josef

doi:10.1007/978-3-662-06863-2

Cited by 56 publications

(27 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…To solve (14), however, we must have a routine to compute all roots, real as well as complex, of a real polynomial. Any textbook on numerical mathematics contains material on this; see for instance STOER (1972). Also, any library of numerical routines such as the NAG or the IMSL library provides adequate software.…”

Section: Unit Claim Amountsmentioning

confidence: 99%

On the Probability and Severity of Ruin

1987

View full text Add to dashboard Cite

In the usual model of the collective risk theory, we are interested in the severity of ruin, as well as its probability. As a quantitative measure, we propose G (u, y), the probability that for given initial surplus u ruin will occur and that the deficit at the time of ruin will be less than y, and the corresponding density g (u, y). First a general answer in terms of the transform is obtained. Then, assuming that the claim amount distribution is a combination of exponential distributions, we determine g; here the roots of the equation that defines the adjustment coefficient play a central role. An explicit answer is also given in the case in which all claims are of constant size. KEYWORDSRuin; severity of ruin.

show abstract

Section: Unit Claim Amountsmentioning

confidence: 99%

On the Probability and Severity of Ruin

1987

View full text Add to dashboard Cite

show abstract

“…Reconsider (3), the adoption of the shooting method and, for example, of the implicit Euler method to determine its large signal steady-state solution § at each time step [10] yields the following equation:…”

Section: The Proposed Methodsmentioning

confidence: 99%

Computation of all the Floquet eigenfunctions in autonomous circuits

Brambilla

Gajani

2007

Circuit Theory & Apps

View full text Add to dashboard Cite

SUMMARYAnalysis methods based on the Floquet theory have gained a large interest to compute small signal and noise effects in non-autonomous and autonomous circuits (oscillators). A reliable and straightforward method to compute all the eigenfunctions related to the Floquet analysis is discussed here. The method has been implemented in a circuit simulator and tested on several circuits. Numerical results are presented.

show abstract

“…The transformation <j)(xi^v) depends on the vectors £ and x and, hence, the matrix <I> depends on these vectors. Without going into detail, we use the results of spline theory [5,6,7] to determine the elements of <&. An implicit assumption must be made about the curve at the endpoints.…”

Section: Bayesian Approach To Background Estimationmentioning

confidence: 99%

“…We choose the natural spline condition, that is, assume that the second derivatives of b(x) are zero at the ends of the interval. Other possible boundary conditions are given in [5,6]. Although the basis set that we consider consists of cubic splines, our approach can be easily adopted to other smooth basis functions.…”

Section: Bayesian Approach To Background Estimationmentioning

confidence: 99%

Bayesian background estimation

Fischer

Dose

Hanson

et al. 2001

AIP Conference Proceedings

View full text Add to dashboard Cite

Abstract. The ubiquitous problem of estimating the background of a measured spectrum is solved with Bayesian probability theory. A mixture model is used to capture the defining characteristics of the problem, namely that the background is smoother than the signal. The smoothness property is quantified in terms of a cubic spline basis where a variable degree of smoothness is attained by allowing the number of knots and the knot positions to be adaptively chosen on the basis of the data. The fully Bayesian approach taken provides a natural way to handle knot adaptivity, allows uncertainties in the background to be estimated and data points to be classified in groups containing only background and groups with additional signal contribution. Our technique is demonstrated on a PIXE spectrum from a geological sample and an Auger spectrum from an 10 monolayer iron film on tungsten.

show abstract

Einführung in die Numerische Mathematik I

Cited by 56 publications

References 0 publications

On the Probability and Severity of Ruin

On the Probability and Severity of Ruin

Computation of all the Floquet eigenfunctions in autonomous circuits

Bayesian background estimation

Contact Info

Product

Resources

About