ERROR ANALYSIS OF SOLUTION FOR GENERALIZED DENSITY EVOLUTION EQUATION VIA A FAMILY OF δ SEQUENCES
To compare with the finite difference method,the solution for a generalized density evolution equation(GDEE) via a family of δ sequences is one of the new and effective numerical methods for GDEE.In order to improve the performance and precision of this new solution,the error analysis is carried out systematically.Firstly,by taking the δ sequences approximation of a probability density function(PDF) as the middle quantity,the error of the solution using δ sequences is divided into two parts.Secondly,the upper bound for the first part of the error is obtained by a mathematical transformation,a replacement and a Taylor expansion,and then the relation and difference between the first part of the error and the error from a kernel density estimation is discussed.Thirdly,the upper bound for the second part of the error is also available by a similar deduction.Finally,it can be found from these results for error analysis that the main influence factors include in the type of δ sequences,the value of λ and the property of the representative point set.And these results present a theoretical basis for the coming parameter analysis of solution using δ sequences.