Abstract
To solve the Fredholm integral equations of the second kind, a new notion of the least-squares orthogonal polynomials of function-valued Pade-type approximation is introduced. On the basis of the error formula, the least-squares function-valued Pade-type approximation is constructed. Their existence and uniqueness are studied. A recursive computation formula of the least-squares function-valued Pade-type approximation is given. In the end, an example is given to show that the method is effective and stable.
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