University of Manchester Best Chebyshev Approximation by Families of Odes with a Xed Initial Condition Best Chebyshev Approximation by Families of Odes with a Xed Initial Condition

Best Chebyshev approximation of real-valued data is treated by approximations obtained from solutions of parameter dependent initial value problems in ordinary diierential equations, in which the initial conditions are speciied. The problem is a modiied form of the problem treated by the authors in 9], 10], and 11]. The xing of the initial condition at t = a requires that approximation be carried out on a set which excludes this point. Numerical examples illustrating the theory are presented.