Epsilon-algorithm and eta-algorithm of generalized inverse function-valued Pade approximants using for solution of integral equations

Two efficient recursive algorithms epsilon-algorithm and eta-algorithm are introduced to compute the generalized inverse function-valued Pade approximants. The approximants were used to accelerate the convergence of the power series with function-valued coefficients and to estimate characteristic value of the integral equations. Famous Wynn identities of the Pade approximants is also established by means of the connection of two algorithms.