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Sequential Monte Carlo for linear systems – a practical summary
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John H. Halton
Published/Copyright:
May 26, 2008
Abstract
This paper has been written in response to many requests for a practical guide to the use of the technique of sequential Monte Carlo in the fast numerical solving of large systems of linear equations. This method, which I have used with considerable success to solve such problems, improving the tricks of the trade as I learned more about it, has suffered from some neglect through the mathematical difficulty, for some of those who are more interested in using the tool than in thinking about it, of some of the theoretical aspects of rigorously proving its validity, which – at this juncture – is no longer in question. I hope that I have now closed this gap in the related literature.
Keywords.: Large linear systems; fast methods of solution; sequential methods; numerical methods; statistical methods; Monte Carlo techniques
Received: 2008-02-26
Revised: 2008-03-24
Published Online: 2008-05-26
Published in Print: 2008-May
© de Gruyter 2008
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Articles in the same Issue
- Sequential Monte Carlo for linear systems – a practical summary
- Some new simulations schemes for the evaluation of Feynman–Kac representations
- Spectra of Perron–Frobenius operator and new construction of two dimensional low discrepancy sequences
- Computing percentage points of the largest among Student's t random variables
- A new nonrecursive pseudorandom number generator based on chaos mappings
Keywords for this article
Large linear systems;
fast methods of solution;
sequential methods;
numerical methods;
statistical methods;
Monte Carlo techniques
Articles in the same Issue
- Sequential Monte Carlo for linear systems – a practical summary
- Some new simulations schemes for the evaluation of Feynman–Kac representations
- Spectra of Perron–Frobenius operator and new construction of two dimensional low discrepancy sequences
- Computing percentage points of the largest among Student's t random variables
- A new nonrecursive pseudorandom number generator based on chaos mappings
