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^ j=i where tj are given points on [a, fo], a = tl<t2<--<tN = b, and Lj and dj are given matrices and vectors, respectively. Some authors have discussed these types of problems and proposed several numerical methods to solve them. Banks and Groome [I] have discussed the quasilinearization algorithm and established the quadratic convergence of it. Urabe [8] has shown that the problem can be reduced to the multipoint boundary value problem of nonlinear boundary condition, and proposed the application of the Newton iterative process. After Urabe's works, Fujii [2] has shown another reduction of the problem to a boundary value problem and discussed the Chebyshev-series-approximation with a-posteriori error bound. In the present paper, we first propose a new method which is an applied version of the initial-value adjusting method given by Ojika and Kasue [6] for

The initial-value adjusting method for problems of the least squares type of ordinary differential equations