## THERMAL SCIENCE

International Scientific Journal

### A REGULARIZED GMRES METHOD FOR INVERSE BLACKBODY RADIATION PROBLEM

**ABSTRACT**

The inverse blackbody radiation problem is focused on determining temperature distribution of a blackbody from measured total radiated power spectrum. This problem consists of solving a first kind of Fredholm integral equation and many numerical methods have been proposed. In this paper, a regularized GMRES method is presented to solve the linear ill-posed problem caused by the discretization of such an integral equation. This method projects the orignal problem onto a lower dimensional subspaces by the Arnoldi process. Tikhonov regularization combined with GCV criterion is applied to stabilize the numerical iteration process. Three numerical examples indicate the effectiveness of the regularized GMRES method.

**KEYWORDS**

PAPER SUBMITTED: 2011-03-16

PAPER REVISED: 2012-04-19

PAPER ACCEPTED: 1970-01-01

**THERMAL SCIENCE** YEAR

**2013**, VOLUME

**17**, ISSUE

**Issue 3**, PAGES [847 - 852]

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