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