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Abstract
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In this paper, a new iterative method is proposed for solving linear integral equations. This
method is based on the LSQR method, an algorithm for sparse linear equations and sparse
least squares, reducing the solution of linear integral equations to the solution of a bidiagonal linear system of algebraic equations. A simple recurrence formula is presented for
generating the sequence of approximate solutions. Some theoretical properties and error
analysis of the new method are discussed. Although the new method can be used for solving the ill-posed first kind integral equations independently, combining of the new method
with the method of regularization is presented to solve this kind of integral equations. Also
the perturbing effect of the first kind integral equations is analyzed. Some properties and
convergence theorem are proposed. Finally, some numerical examples are presented to
show the efficiency of the new method.
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