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Fredholm resolvents, Wiener-Hopf equations, and Riccati differential equations

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1 Author(s)
Kailath, T. ; Stanford University, Stanford, CA, USA

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 least-squares 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.

Published in:

Information Theory, IEEE Transactions on  (Volume:15 ,  Issue: 6 )

Date of Publication:

Nov 1969

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