Abstract
In this paper we investigate the quadratic model bTu+uTCu aTU' which generalises the Shanks transformation and the familiar Pade model, to accelerate the conver-gence of a sequence {uk}kEZP. In the new model, u T =[u0, u 1>~ ,Tln,1, a, b E R+1 and C is an (n + 1) x (n + 1) Hermitian matrix. (Note that, although u might be complex, we use the transpose uT, rather than the adjoint u*.) Let us assume that the original sequence is obtained from the dynamical system z H f (z), where f (z) = v, + E~ 1 k, i3k (z - u)k is analytic about its fixed point u E C. Suppose that uo = u -f a and uk = f°k(uo). It is easy to show that b = 0 and a = 2C1. We give an iterative formula for the construction of the matrices C. Fhrthermore, we discuss the rate of convergence, inclusive of the special case when the fixed point is at oo.
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