Reply to the comments on “The boundary point method for the calculation of exterior acoustic radiation” (by S.Y. Zhang, X.Z. Chen, Journal of Sound and Vibration 228(4) (1999) 761–772)

2006 ◽  
Vol 298 (4-5) ◽  
pp. 1174-1175
Author(s):  
X.Z. Chen ◽  
C.X. Bi
Keyword(s):  
Boundary Point ◽  
Acoustic Radiation ◽  
Point Method ◽  
Boundary Point Method

scholarly journals A Modified Mann Iteration by Boundary Point Method for Finding Minimum-Norm Fixed Point of Nonexpansive Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Songnian He ◽  
Wenlong Zhu
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Boundary Point ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Point Method ◽  
Minimum Norm ◽  
Mann Iteration ◽  
Boundary Point Method

LetHbe a real Hilbert space andC⊂H a closed convex subset. LetT:C→Cbe a nonexpansive mapping with the nonempty set of fixed pointsFix(T). Kim and Xu (2005) introduced a modified Mann iterationx0=x∈C,yn=αnxn+(1−αn)Txn,xn+1=βnu+(1−βn)yn, whereu∈Cis an arbitrary (but fixed) element, and{αn}and{βn}are two sequences in(0,1). In the case where0∈C, the minimum-norm fixed point ofTcan be obtained by takingu=0. But in the case where0∉C, this iteration process becomes invalid becausexnmay not belong toC. In order to overcome this weakness, we introduce a new modified Mann iteration by boundary point method (see Section 3 for details) for finding the minimum norm fixed point of Tand prove its strong convergence under some assumptions. Since our algorithm does not involve the computation of the metric projectionPC, which is often used so that the strong convergence is guaranteed, it is easy implementable. Our results improve and extend the results of Kim, Xu, and some others.

Orthogonal spherical wave source boundary point method and its application to acoustic holography

2004 ◽  
Vol 49 (16) ◽  
pp. 1758-1767 ◽  
Author(s):  
Chuanxing Bi ◽  
Xinzhao Chen ◽  
Jian Chen ◽  
Weibing Li
Keyword(s):  
Boundary Point ◽  
Spherical Wave ◽  
Point Method ◽  
Acoustic Holography ◽  
Wave Source ◽  
Boundary Point Method
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