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Backward Error Analysis in Computational Geometry
[chapter]

2006
*
Lecture Notes in Computer Science
*

In this paper it will be shown how the now-classical

doi:10.1007/11751540_6
fatcat:35pwzjxwuja5rdbms43rnnb5ie
*backward**error**analysis*can be applied in the area of computational geometry. ... The exposition will illustrate the fact that the*backward**error**analysis*does not pretend*to*overcome the problem of finite precision: it merely provides a tool*to*distinguish, in a fairly routine way, ... This is a pure*backward**error**analysis*, with a well-conditioned problem. ...##
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FLOATING-POINT ARITHMETIC FOR COMPUTATIONAL GEOMETRY PROBLEMS WITH UNCERTAIN DATA

2009
*
International journal of computational geometry and applications
*

It is first shown how the now-classical

doi:10.1142/s0218195909003015
fatcat:wwobyql2pvebnooc3fn6uic2f4
*backward**error**analysis*can be applied in the area of computational geometry. ... The exposition will illustrate the fact that the*backward**error**analysis*does not pretend*to*overcome the problem of finite precision: it merely provides a way*to*distinguish those algorithms that overcome ... This is a pure*backward**error**analysis*, with a well-conditioned problem. ...##
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Dedication

1987
*
Linear Algebra and its Applications
*

His 1961 paper, "Error Analysis of Direct Methods of Matrix Inversion," in the Journal of the ACM, marks the beginning of the Wilkinson error analysis and his use of "

doi:10.1016/0024-3795(87)90098-x
fatcat:5pe47s6gx5awrc5jghsi2j4fym
*backward**error**analysis*." ... He was also a frequent visitor*to*many other parts of the world, having colleagues and friends in dozens of countries, and enjoyed summer camping trips*to*the south of France. ... Jim*replied*, "Yes, I assume it is, but it has never been one of my ambitions." This genial man has left us all much richer by his technical achievements and his warm, giving spirit. ...##
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Numerical Software: Science or Alchemy?
[chapter]

1980
*
Advances in Computers
*

That is why

doi:10.1016/s0065-2458(08)60035-2
fatcat:ovpihqr4kbd47fhjla2yxwlxui
*backward**error**analysis*is such a handy tool. ... In forward error analysis we try*to*determine the size of z -y, whereas in*backward**error**analysis*, we ask how big Ad has*to*be in order that P[d + Ad,z] = 0 The advantage of*backward**error**analysis*is ... Report has been sent*to*responsible AEC patent group for clearance. I I c. Patent clearance not required. ...##
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Approximating the Value of a Concurrent Reachability Game in the Polynomial Time Hierarchy
[chapter]

2013
*
Lecture Notes in Computer Science
*

We show that the value of a finite-state concurrent reachability game can be approximated

doi:10.1007/978-3-642-45030-3_43
fatcat:nrdxo2ta2fgzxagfzaunx3jefi
*to*arbitrary precision in TFNP [NP], that is, in the polynomial time hierarchy. ... ABSORPTION is applied*to*M (x, y), its estimate for this probability has error much smaller than 2 −k−3 , that is, its estimate is larger than v − 2 −k−2 . ... We emphasize that the adaptation is standard in the context of numerical analysis -in particular, the error analysis is an instance of the*backward**error**analysis*paradigm due*to*Wilkinson [15] -but ...##
###
Page 969 of Mathematical Reviews Vol. 32, Issue Index
[page]

*
Mathematical Reviews
*

R. et al., (2000f:37004)
Guckenheimer, J. see Choe, Won Gyu, 2000m:65093
Hairer, Ernst

*Backward**error**analysis*for multistep methods. (English summary) 2000k:65111 Herbst, B. ...*Reply**to*: “Comment on ‘Self-similarity and transport in the standard map’ ” [Phys. Rev. E (3) 59 (1999), no. 3, part B, 3756-3760; MR 2000h:37049a] by G. Zumofen and J. Klafter. ...##
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Page 663 of Mathematical Reviews Vol. 17, Issue Index
[page]

*
Mathematical Reviews
*

*Backward*

*error*

*analysis*for linear systems associated with inverses of H-matrices. BIT 24 (1984), no. 1, 102-112. (E. L. ... A service model in which the server is required

*to*search for customers. J. Appl. Probab. 21 (1984), no. 1, 157-166. (Carl M. ...

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John von Neumann's Analysis of Gaussian Elimination and the Origins of Modern Numerical Analysis

2011
*
SIAM Review
*

be needed

doi:10.1137/080734716
fatcat:6ymfptvzfrg7doc7ajv4iljk24
*to*use the new machines effectively and*to*guide the development of still faster computers. ... Von Neumann once remarked that*to*found a mathematical theory one had*to*prove the first theorem, which he and Goldstine did for the accuracy of mechanized Gaussian elimination-but their paper was about ... Invention of*Backward**Error**Analysis*. A few years after the inversion paper, Givens referred*to*the sources of error by the letters (A)-(D) that von Neumann and Goldstine had used. ...##
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Computational topology
[chapter]

2007
*
Open Problems in Topology II
*

What are the differing floating point precisions needed

doi:10.1016/b978-044452208-5/50049-1
fatcat:42tc4oklkneujkowb7s4aburfi
*to*capture 1111? ... Will the process of finding the precision required for the models for these engineering simulations generalize*to*a mathematical methodology for being able*to*determine floating point precision needs for ... Thanks are also due*to*Ralph Kopperman and Yuriy Mileyko for numerous helpful conversations. ...##
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Soft Error Resilient Time Stepping Schemes on Regular Grids

2016

Large cluster computer suitable for such calculations are subject

doi:10.3929/ethz-a-010583223
fatcat:zm7o5wh265bwvhqv4k4mwo4jma
*to*frequent failures due*to*their myriad of components. ... This solution is projected*to*come*to*a halt in the near future because of unfortunate developments of failure rate, snapshot size and the storage bandwidth. ... Acknowledgements 33 References 33 Acknowledgements I would like*to*thank the following people for helping me in various phases during this thesis: Peter Arbenz for the opportunity of this project and the ...##
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OASIcs, Volume 86, Gabbrielli's Festschrift, Complete Volume
[article]

2020

Acknowledgements We are very pleased

doi:10.4230/oasics.gabbrielli
fatcat:quirdjgconeajayodg7uri43x4
*to*dedicate this work*to*Maurizio, whose notable contributions*to*the theory of programming languages are well known and appreciated by the scientific community. ... We would like*to*thank the anonymous referees for their helpful comments. ... In summary, while there are important relations with other parts of mathematics, like numerical analysis (e.g., Jim Wilkinson's*backward**error**analysis*), or automata theory (from von Neumann,*to*Kleene's ...