In this chapter we shall give some simple examples to illustrate the meaning of the theorems and the computations performed by the algoritms. The reader should be warned for the poor numerical performance of these algorithms when implemented in finite arithmetic. Only for the positive definite case considered in previous chapter, the Levinson and Schur algorithm can be considered to be numerically stable [CYB,BU10]. To avoid numerical difficulties, we shall give examples that are computable in exact arithmetic.
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