New matrix method for multipoint Padé approximation of transfer functions

T. Nigel Lucas

Research output: Contribution to journal › Article

  • 3 Citations

Abstract

A new way of formulating a multipoint Padé approximant of a linear system transfer function is given. It is seen to be very flexible and computationally efficient. The expansion points can be a mixture of real, complex, purely imaginary and multiple points with no complex arithmetic required. The underlying idea of the method is to convert the rational approximation problem into one of polynomial approximation. This results in simple matrix multiplications and the solution of a set of linear equations to derive the reduced model. Examples are given to demonstrate the application of the technique.
Original languageEnglish
Pages (from-to)809-818
Number of pages10
JournalInternational Journal of Systems Science
Volume24
Issue number5
DOIs
StatePublished - 1993

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Transfer function
Transfer functions
Padé approximation
Padé approximants
Matrix multiplication
Reduced model
Rational approximation
Approximation problem
Matrix method
Polynomial approximation
Convert
Linear equation
Linear systems
Demonstrate
Linear equations

Cite this

Lucas, T. Nigel / New matrix method for multipoint Padé approximation of transfer functions.

In: International Journal of Systems Science, Vol. 24, No. 5, 1993, p. 809-818.

Research output: Contribution to journal › Article

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Lucas, TN 1993, 'New matrix method for multipoint Padé approximation of transfer functions' International Journal of Systems Science, vol 24, no. 5, pp. 809-818. DOI: 10.1080/00207729308949525

New matrix method for multipoint Padé approximation of transfer functions. / Lucas, T. Nigel.

In: International Journal of Systems Science, Vol. 24, No. 5, 1993, p. 809-818.

Research output: Contribution to journal › Article

TY - JOUR

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AU - Lucas,T. Nigel

PY - 1993

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N2 - A new way of formulating a multipoint Padé approximant of a linear system transfer function is given. It is seen to be very flexible and computationally efficient. The expansion points can be a mixture of real, complex, purely imaginary and multiple points with no complex arithmetic required. The underlying idea of the method is to convert the rational approximation problem into one of polynomial approximation. This results in simple matrix multiplications and the solution of a set of linear equations to derive the reduced model. Examples are given to demonstrate the application of the technique.

AB - A new way of formulating a multipoint Padé approximant of a linear system transfer function is given. It is seen to be very flexible and computationally efficient. The expansion points can be a mixture of real, complex, purely imaginary and multiple points with no complex arithmetic required. The underlying idea of the method is to convert the rational approximation problem into one of polynomial approximation. This results in simple matrix multiplications and the solution of a set of linear equations to derive the reduced model. Examples are given to demonstrate the application of the technique.

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DO - 10.1080/00207729308949525

M3 - Article

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JO - International Journal of Systems Science

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JF - International Journal of Systems Science

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IS - 5

ER -

Lucas TN. New matrix method for multipoint Padé approximation of transfer functions. International Journal of Systems Science. 1993;24(5):809-818. Available from, DOI: 10.1080/00207729308949525

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