# VFIT3

VFIT3.zip cointains version 1.0 of vectfit3 (routine: vectfit3.m). The examples show how to fit scalars, columns and entire matrices, and how to formulate the model in the form of state-space models and pole-residue models.

This package (VFIT3.zip) guide contains a Matlab routine vectfit3.m, which is an implementation of FRVF (Fast Relaxed Vector Fitting). vectfit3 computes a rational approximation from tabulated data in the frequency domain. It is intended to replace the previous vectfit2.m (2005). vectfit3 offers superior speed when fitting elements with many elements due to a fast implementation of the pole identification step.

The function to be fitted can be either a single frequency response, or a vector of frequency responses. In the latter case, all elements in the vector will be fitted using a common pole set. The resulting model can be expressed in either state-space form or pole-residue form.

• Vector Fitting (VF) [1] iteratively relocates an initial set of poles to better positions by solving a linear least squares problem. Stable poles is ensured by pole flipping. The pole identification is followed by a residue identifications step. (A single call to vectfit3 gives a single iteration).
• A relaxed non-triviality constraint [2] is used in the pole identification step of VF for achieving faster convergence and less biasing [2].
• The linear problem associated with the pole identification step of VF is solved in a fast way by utilizing the matrix structure [3].

Restrictions of use:

• Embedding the program code (vectfit3.m) in any commercial software is strictly prohibited.
• If the code is used in a scientific work, then reference should me made to the following three publications:

1. B. Gustavsen and A. Semlyen, "Rational approximation of frequency domain responses by Vector Fitting", IEEE Trans. Power Delivery, vol. 14, no. 3, pp. 1052-1061, July 1999. Link
2. B. Gustavsen, "Improving the pole relocating properties of vector fitting", IEEE Trans. Power Delivery, vol. 21, no. 3, pp. 1587-1592, July 2006. Link
3. D. Deschrijver, M. Mrozowski, T. Dhaene, and D. De Zutter, “Macromodeling of  Multiport Systems Using a Fast Implementation of the Vector Fitting Method”, IEEE Microwave and Wireless Components Letters, vol. 18, no. 6, pp. 383-385, June 2008. Link