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Calling Sequence
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hermite_pade([f1, f2,..., fn], x, N)
hermite_pade([f1, f2,..., fn], x, [d1, d2,..., dn])
hermite_pade([f1, f2,..., fn], x=a, N)
hermite_pade([f1, f2,..., fn], x=a, [d1, d2,..., dn])
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Parameters
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f1, ..., fn
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expressions representing the functions to be approximated
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x
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the variable appearing in the f_i's
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a
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the point about which to expand in a series
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N
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non-negative integer
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d1, ..., dn
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degree bounds
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Description
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The function hermite_pade computes a Hermite-Pade approximation of degree (d1,..., dn) for the functions f1,..., fn with respect to the variable x. When the degrees are not specified, but rather the order N is given, then an approximation of minimal degree is computed.
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Specifically, f1,..., fn are expanded in Taylor series about the point (if a is not specified then the expansion is about the point ), to order , and then the Hermite-Pade rational approximation is computed.
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The (d1,..., dn) Hermite-Pade approximation is defined to be the list of polynomials with such that the Taylor series expansion of has maximal valuation at .
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Various levels of user information will be displayed during the computation if infolevel[hermite_pade] is assigned values between 1 and 3.
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This code is based on a procedure by H. Derksen in previous versions of the share library.
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The command with(numapprox,hermite_pade) allows the use of the abbreviated form of this command.
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Examples
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>
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>
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>
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>
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References
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Beckermann, B., and Labahn, G. "A uniform approach for Hermite Pade and simultaneous Pade approximants and their matrix-type generalizations." Numerical Algorithms, Vol. 3, (1992): 45-54.
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Beckermann, B., and Labahn, G. "A uniform approach for the fast computation of matrix-type Pade approximants." SIAM Journal on Matrix Analysis and Applications, Vol. 15, No. 3, (1994): 804-823.
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Derksen,H. An algorithm to compute generalized Pade-Hermite forms. 1994. Available at http://www.math.lsa.umich.edu/~hderksen/preprints/pade.dvi.
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