An example of the wavelet impedance matrix with O(N) nonzero elements

✍ Scribed by Gaofeng Wang; Bing-Zhong Wang; Jiechang Hou

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 75 KB
• Volume: 14
• Category: Article
• ISSN: 0895-2477
• DOI: 10.1002/(sici)1098-2760(19970220)14:3<181::aid-mop14>3.0.co;2-b

✦ Synopsis

By the use of wa¨elet basis functions, an integral equation can be con¨erted into a sparse matrix equation after discretization. Through the exploitation of the sparsity of the impedance matrix, the complexity of sol¨ing the resultant matrix equation can be greatly reduced. It has been reported that the number of nonzero elements in a 2 ( ) wa¨elet impedance matrix is ␣ N 0F␣F1 , where ␣ is approximately a constant. This implies that sol¨ing the sparse matrix equation produced by a wa¨elet expansion has the same complexity as sol¨ing a full matrix. In this Letter, howe¨er, we present an example of the wa¨elet ( ) impedance matrix that results in a much lower complexityᎏO N . ᮊ