Browsing by Author "Lucas, T. Nigel"
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Finding roots by deflated polynomial approximation
Lucas, T. Nigel (Elsevier, 1990)A numerical technique is presented which evaluates the roots of polynomials with real coefficients. Features of the method include no complex arithmetic requirements, no need to guess at initial quadratic factor estimates, ... 
Finding roots of polynomials by using the Routh array
Lucas, T. Nigel (Institution of Engineering and Technology, 199608)A robust method for finding the roots of polynomials using the Routh array is given. Certain multipoint approximation properties of the array are clarified, which enable a simple criterion to be used in the rootfinding ... 
Flexible timeresponse matching in discrete model reduction
Lucas, T. Nigel (Sage Publications, 200008)A simple way to match the time responses of the full and reducedorder models at arbitrary sampling points is given for discretetime systems. It is seen to be a natural extension of the Padé methods and is particularly ... 
Frequencydomain reduction of linear systems using Schwarz approximation
Lucas, T. Nigel; Davidson, A. M. (Taylor & Francis, 1983)A frequency domain approach for reducing linear, timeinvariant systems is presented which produces stable approximations of stable systems. The method is based upon the Schwarz canonical form and is shown to have a ... 
Further discussion on impulse energy approximation
Lucas, T. Nigel (Institute of Electrical and Electronics Engineers, 198702)Recent criticisms by Rao about impulse energy approximation are answered in detail. Further ideas are put forward as to how weighted energy parameters may be used to determine the reduced models for step inputs. 
Leastsquares moment matching reduction methods
Smith, I. D.; Lucas, T. Nigel (Institution of Engineering and Technology, 199505)It is shown how the two apparently different approaches to modelling reduction by leastsquares time moment matching give identical results. This property also enables a clear understanding of how the method actually ... 
Leastsquares Pade reduction: a nonuniqueness property
Lucas, T. Nigel; Smith, I. D. (Institution of Engineering and Technology, 199509)It is shown that leastsquares Pade reduced order models are not unique for a given order. Depending on which reduced denominator coefficient is chosen to be unity. The method is seen to minimise an error index over different ... 
Linear system reduction by continuedfraction expansion about s = 0 and s = a alternately
Lucas, T. Nigel (Institution of Engineering and Technology, 198303)A method of reduction is given which uses the concept of expanding the system transfer function about the origin and about a general point. This results in good overall responses, and families of reduced models of the same ... 
Linear system reduction by continuedfraction expansion about three points
Lucas, T. Nigel (Institution of Engineering and Technology, 198401)The method of model reduction by continuedfraction expansion about s = 0 and s = a is extended to include the point s = Ã Â¿ also. This achieves more accurate transient approximations and thus highlights further the ... 
Linear system reduction by impulse energy approximation
Lucas, T. Nigel (Institute of Electrical and Electronics Engineers, 198508)A method is given for linear system reduction which is a more general form of the Routh method. The reduced models retain stability, and a fuller contribution is made to the impulse response energy of the reduced system ... 
Linear system reduction by the modified factor division method
Lucas, T. Nigel (Institution of Engineering and Technology, 198611)A novel method of linear system simplification is presented based on a modified factor division approach. It is seen to be more flexible than most model reduction methods in that families of reduced models may be easily ... 
Linear system reduction using Schwarz canonical form
Davidson, A. M.; Lucas, T. Nigel (Institution of Engineering and Technology, 197606)A system reduction method based on Schwarz canonical form has recently been observed to have certain momentmatching properties. By reformulating the method, these properties are proved and extended and the stability of ... 
Linearsystem reduction by continuedfraction expansion about a general point
Davidson, A. M.; Lucas, T. Nigel (Institution of Engineering and Technology, 197407)Capacity requirements for multipleaccess demandassigned communication systems are broken down into information, demand and assignment signalling. A simultaneoustransmission scheme for demand signalling greatly reduces ... 
Model reduction by condensed continuedfraction method
Lucas, T. Nigel (Institution of Engineering and Technology, 198508)It is shown how the continuedfraction method of Chen and Shieh may be used on part of the transfer function to produce reducedorder models when its normal application is unsatisfactory. In addition, the truncation method ... 
Model reduction by generalised leastsquares method
Lucas, T. Nigel; Munro, A. R. (Institution of Engineering and Technology, 199107)The method of model reduction by leastsquares moment matching is generalised to include Markov parameters in the process. This is seen to enhance the flexibility of the method with very little extra computational requirement. ... 
Model reduction by leastsquares moment matching
Lucas, T. Nigel; Beat, I. F. (Institution of Engineering and Technology, 199007)Model reduction by leastsquares moment matching is shown to be very sensitive to the pole distribution of the original system. Systems with poles of modulus less than unity are seen to present numerical problems. A ... 
Modelling an athletics track
Lucas, T. Nigel (Oxford University Press, 1991)When introducing students to mathematical modelling ideas it is often useful to have them tackle a fairly "welldefined" problem, possibly related to an outside interest, involving the use of traditional mathematical ... 
New matrix method for multipoint Pade approximation of transfer functions
Lucas, T. Nigel (Taylor & Francis, 1993)A new way of formulating a multipoint Pad 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, ... 
New results on relationships between multipoint Pade approximation and stability preserving methods in model reduction
Lucas, T. Nigel (Taylor & Francis, 1989)Three wellknown stability preserving methods of reduction are shown to be special forms of the multipoint pade approximation. Two of the methods—the modified forms of the Schwarz approximation and the stability equation ... 
A note on order reduction by the discretetime leastsquares Padé method
Lucas, T. Nigel (Sage Publications, 1999)It is shown that reduced order models produced by the leastsquares Padé method for discretetime systems can sometimes produce misleading results for step and polynomial inputs. A more representative way of deriving such ...