# IJPAM: Volume 62, No. 1 (2010)

**COLLOCATION METHOD FOR SOLVING SOME INTEGRAL**

EQUATIONS OF ESTIMATION THEORY

EQUATIONS OF ESTIMATION THEORY

Department of Mathematics

Kansas State University

Manhattan, KS 66506-2602, USA

e-mail: [email protected]

**Abstract.**A class of integral equations basic in
estimation theory is introduced. The description of the range
of the operator is given. The operator is a positive rational
function of a selfadjoint elliptic operator .
This operator is defined in the whole space , it has a kernel
, and
, where
is a bounded domain with a sufficiently smooth boundary .
Example of the equation of this type is
This equation
has, in general, only distributional solutions. In estimation theory
one is interested in the MOS (minimal order of singularity) solution to
equation . It is proved that such solution does exist and is unique
for the class of equations defined by the author.
A collocation method for numerical solution of equation
in distributions is
formulated and its convergence is proved.

**Received: **May 25, 2010

**AMS Subject Classification: **162H12, 62M20, 62M40, 65R20, 45P05

**Key Words and Phrases: **estimation theory, integral equations, collocation method, distributional solution

**Source:** International Journal of Pure and Applied Mathematics

**ISSN:** 1311-8080

**Year:** 2010

**Volume:** 62

**Issue:** 1