TY - GEN
T1 - Prony systems via decimation and homotopy continuation
AU - Batenkov, Dmitry
PY - 2014
Y1 - 2014
N2 - We consider polynomial systems of Prony type, appearing in many areas of mathematics. Their robust numerical solution is considered to be dificult, especially in\near-colliding" situations. We transform the nonlinear part of the Prony system into a Hankel-type polynomial system. Combining this representation with a recently discovered \decimation" technique, we present an algorithm which applies homotopy continuation on a sequence of modified Hankel-type systems as above. In this way, we are able to solve for the nonlinear variables of the original system with high accuracy when the data is perturbed.
AB - We consider polynomial systems of Prony type, appearing in many areas of mathematics. Their robust numerical solution is considered to be dificult, especially in\near-colliding" situations. We transform the nonlinear part of the Prony system into a Hankel-type polynomial system. Combining this representation with a recently discovered \decimation" technique, we present an algorithm which applies homotopy continuation on a sequence of modified Hankel-type systems as above. In this way, we are able to solve for the nonlinear variables of the original system with high accuracy when the data is perturbed.
KW - Decimation
KW - Prony systems
UR - http://www.scopus.com/inward/record.url?scp=84906311268&partnerID=8YFLogxK
U2 - 10.1145/2631948.2631961
DO - 10.1145/2631948.2631961
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AN - SCOPUS:84906311268
SN - 9781450329637
T3 - Proceedings of the 2014 Symposium on Symbolic-Numeric Computation, SNC 2014
SP - 59
EP - 60
BT - Proceedings of the 2014 Symposium on Symbolic-Numeric Computation, SNC 2014
PB - Association for Computing Machinery
T2 - 2014 Symposium on Symbolic-Numeric Computation, SNC 2014
Y2 - 28 July 2014 through 31 July 2014
ER -