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Backward Error Analysis in Computational Geometry [chapter]

Di Jiang, Neil F. Stewart
2006 Lecture Notes in Computer Science  
In this paper it will be shown how the now-classical 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.  ... 
doi:10.1007/11751540_6 fatcat:35pwzjxwuja5rdbms43rnnb5ie

FLOATING-POINT ARITHMETIC FOR COMPUTATIONAL GEOMETRY PROBLEMS WITH UNCERTAIN DATA

D. JIANG, N. F. STEWART
2009 International journal of computational geometry and applications  
It is first shown how the now-classical 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.  ... 
doi:10.1142/s0218195909003015 fatcat:wwobyql2pvebnooc3fn6uic2f4

Dedication

Gene H. Golub, Cleve Moler
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 "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.  ... 
doi:10.1016/0024-3795(87)90098-x fatcat:5pe47s6gx5awrc5jghsi2j4fym

Numerical Software: Science or Alchemy? [chapter]

C.W. Gear
1980 Advances in Computers  
That is why 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.  ... 
doi:10.1016/s0065-2458(08)60035-2 fatcat:ovpihqr4kbd47fhjla2yxwlxui

Approximating the Value of a Concurrent Reachability Game in the Polynomial Time Hierarchy [chapter]

Søren Kristoffer Stiil Frederiksen, Peter Bro Miltersen
2013 Lecture Notes in Computer Science  
We show that the value of a finite-state concurrent reachability game can be approximated 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  ... 
doi:10.1007/978-3-642-45030-3_43 fatcat:nrdxo2ta2fgzxagfzaunx3jefi

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.  ... 

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.  ... 

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

Joseph F. Grcar
2011 SIAM Review  
be needed 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.  ... 
doi:10.1137/080734716 fatcat:6ymfptvzfrg7doc7ajv4iljk24

Computational topology [chapter]

Denis Blackmore, Thomas J. Peters
2007 Open Problems in Topology II  
What are the differing floating point precisions needed 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.  ... 
doi:10.1016/b978-044452208-5/50049-1 fatcat:42tc4oklkneujkowb7s4aburfi

Soft Error Resilient Time Stepping Schemes on Regular Grids

Manuel Christoph Kohler
2016
Large cluster computer suitable for such calculations are subject 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  ... 
doi:10.3929/ethz-a-010583223 fatcat:zm7o5wh265bwvhqv4k4mwo4jma

OASIcs, Volume 86, Gabbrielli's Festschrift, Complete Volume [article]

Frank S. de Boer, Jacopo Mauro
2020
Acknowledgements We are very pleased 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  ... 
doi:10.4230/oasics.gabbrielli fatcat:quirdjgconeajayodg7uri43x4