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THE AVERAGE CASE COMPLEXITY OF THE SHIFT-INVARIANT PROBLEM 被引量:1
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作者 Arthur.G.Werschulz 《Analysis in Theory and Applications》 1998年第1期1-7,共0页
The present paper deals with the average case complexity of the shift—invariant problem. The main aim is to give a new proof of the upper bound of average error of finite element method. Our method is based on the te... The present paper deals with the average case complexity of the shift—invariant problem. The main aim is to give a new proof of the upper bound of average error of finite element method. Our method is based on the techniques proposed by Heinrich (1990). We also point out an essential error regarding the proof of the upper bound in A. G. Werschulz (1991). 展开更多
关键词 FEM THE AVERAGE CASE COMPLEXITY OF THE SHIFT-INVARIANT PROBLEM
全文增补中
Dynamical intricacy and average sample complexity of amenable group actions
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作者 Jie Li Siming Tu 《Science China Mathematics》 SCIE CSCD 2022年第6期1247-1266,共20页
In 2018,Petersen and Wilson introduced the notion of dynamical intricacy and average sample complexity for dynamical systems of Z-action,based on the past works on the notion of intricacy in the research of brain netw... In 2018,Petersen and Wilson introduced the notion of dynamical intricacy and average sample complexity for dynamical systems of Z-action,based on the past works on the notion of intricacy in the research of brain network and probability theory.If one wants to take into account underlying system geometry in applications,more general group actions may need to be taken into consideration.In this paper,we consider this notion in the case of amenable group actions.We show that many basic properties in the Z-action case remain true.We also show that their suprema over covers or partitions are equal to the amenable topological entropy and the measure entropy,using the quasitiling technique in the theory of the amenable group. 展开更多
关键词 intricacy average sample complexity topological entropy amenable group
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COMPLEX INNER PRODUCT AVERAGING METHOD FOR CALCULATING NORMAL FORM OF ODE
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作者 CHEN Yu-shu(陈予恕) +1 位作者 SUN Hong-jun(孙洪军) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第12期1368-1374,共7页
This paper puts forward a complex inner product averaging method for calculating normal form of ODE. Compared with conventional averaging method, the theoretic analytical process has such simple forms as to realize co... This paper puts forward a complex inner product averaging method for calculating normal form of ODE. Compared with conventional averaging method, the theoretic analytical process has such simple forms as to realize computer program easily. Results can be applied in both autonomous and non-autonomous systems. At last, an example is resolved to verify the method. 展开更多
关键词 nonlinear dynamic system normal form complex inner product averaging method
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