FREDHOLM RESOLVENTS, WIENER-HOPF EQUATIONS, AND RICCATI DIFFERENTIAL EQUATIONS

被引:40
作者
KAILATH, T
机构
[1] Department of Electrical Engineering, Stanford University, Stanford, Calif.
关键词
D O I
10.1109/TIT.1969.1054367
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
We shall show that the solution of Fredholm equations with symmetric kernels of a certain type can be reduced to the solution of a related Wiener-Hopf integral equation. A leastsquares filtering problem is associated with this equation. When the kernel has a separable form, this related problem suggests that the solution can be obtained via a matrix Riccati differential equation, which may be a more convenient form for digital computer evaluation. The Fredholm determinant is also expressed in terms of the solution to the Riccati equation; this formula can also be used for the numerical determination of eigenvalues. The relations to similar work by Anderson and Moore and by Schumitzky are also discussed. © 1969 IEEE. All Rights Reserved.
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页码:665 / +
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