Several aspects of the conditioning of the Padé approximation problem are considered. The first is concerned with the operator that associates a power series f with its Padé approximant of a certain order. It is shown that this operator satisfies a local Lipschitz condition, in case the Padé approximant is normal.
The second aspect is the conditioning of the Padé approximant itself. It is indicated how this rational function r should be represented such that changes in its coefficients will effect changes on r as less as possible. A “condition number” for this problem is introduced.
The third aspect is the problem of the representation of the Padé approximant, such that the determination of its coefficients be a well-conditioned problem. It is known that the choice of powers of x as base functions can result in an ill-conditioned problem for the determination of the coefficients. The possibility of using other base functions is analysed.
Base Function Rational Function Condition Number Toeplitz Matrix Hankel Matrix
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