A CLASS OF BASES IN L2 FOR THE SPARSE REPRESENTATION OF INTEGRAL-OPERATORS
A CLASS OF BASES IN L2 FOR THE SPARSE REPRESENTATION OF INTEGRAL-OPERATORS
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DOI：
10.1137/0524016
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发表时间：
1993-01-01
影响因子：
2
通讯作者：
ALPERT, BK
中科院分区：
文献类型：
--
作者：
ALPERT, BK
构造了一类L2的多小波基，其性质是将各种积分算子表示为稀疏矩阵，具有较高的精度。具体地说，除了沿着有限数目的奇异带外，其核是光滑的积分算子K具有稀疏表示。此外，涉及K的第二类积分方程解中出现的逆算子(I-K)-1在新的基上往往是稀疏的。得到了求解一大类第二类积分方程数值解的O(n，log2，n)阶算法。
A class of multiwavelet bases for L2 is constructed with the property that a variety of integral operators is represented in these bases as sparse matrices, to high precision. In particular, an integral operator K whose kernel is smooth except along a finite number of singular bands has a sparse representation. In addition, the inverse operator (I - K)-1 appearing in the solution of a second-kind integral equation involving K is often sparse in the new bases. The result is an order O(n log2 n) algorithm for numerical solution of a large class of second-kind integral equations.