## Proceedings of the International School of Physics "Enrico Fermi". |

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Page 60

6) Propagation errors, which are due to the iterative nature of numerical

... Eoughly speaking, the numerical stability of a

...

6) Propagation errors, which are due to the iterative nature of numerical

**methods**.... Eoughly speaking, the numerical stability of a

**method**can be defined as the**method's**capability of damping any perturbation few steps farther the point where...

Page 62

The following iteration formula is then assumed for denning the numerical

approximation to y: (3.8) un+1 = u„ — Xhctxun — AfcaaMB+1 , aa + a, = 1, a#>0,

» = 1, 2, which entails (3-9) w" = lrT^)y°- It can be easily seen that the

The following iteration formula is then assumed for denning the numerical

approximation to y: (3.8) un+1 = u„ — Xhctxun — AfcaaMB+1 , aa + a, = 1, a#>0,

» = 1, 2, which entails (3-9) w" = lrT^)y°- It can be easily seen that the

**method**is ...Page 65

i) Keeping under control stiffness by means of an implicit

the linear algebraic system the implicit

common to all noteworthy

i) Keeping under control stiffness by means of an implicit

**method**. ii) Triangulatingthe linear algebraic system the implicit

**method**leads to. Actions i) and ii) arecommon to all noteworthy

**methods**for numerically handling Markov equations, ...### What people are saying - Write a review

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### Contents

System Eeliabujty | 3 |

Statistical Theory of Eeliablitt | 8 |

Definitions and characterizations | 12 |

Copyright | |

39 other sections not shown

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### Common terms and phrases

algorithm approach associated assume assumption Bayesian boundary points chain coherent system complex conjugate prior consider correctness defined denote detected discussed edited equations equivalence class ergodic errors example exponential distribution failure rate Fault Tree Analysis function gamma given human reliability IEEE Trans IFEA implementation increasing independent input domain integration interval likelihood Markov Markov chain matrix mean method modules monotone month2 N. D. Singpurwalla number of failures number of system NUMITEMS observed obtained operational output parameters phase Poisson Poisson process possible predictive prior distribution probability problem procedure Proschan R. E. Barlow random variables reliability growth models reliability theory renewal theory repair requirements sample sect sequence Software Eng software reliability software reliability models specification Stat statistical stochastic stochastic process subsection system failure system reliability techniques theorem tion tt tt values vector zero