ABSTRACT
The solution functions in a boundary value problem are approximated by Chebyshev series. The reason why catastrophic cancellation arises in computing residual is analyzed, for the system of the algebraic equations, whose unknowns consist of Chebyshev coefficients. It is shown to be due to roundoff errors of floating-point additions. The algorithm computing high accuracy round-off errors of residual is obtained, by the method that all possible errors arising from floating-point arithmetic errors and propagation errors are gathered and those are added by the higher accuracy precision.
