|For repeated roots, resi2 computes the residues at the repeated root locations||Problem formulations making use of state-space or zero-pole representations are preferable|
For most textbook problems, k s is 0 or a constant.
|, p 1 are the poles, and k s is a polynomial in s||The number of poles n is Algorithms residue first obtains the poles using roots|
|Numerically, the partial fraction expansion of a ratio of polynomials represents an ill-posed problem||Finally, residue determines the residues by evaluating the polynomial with individual roots removed|
If the denominator polynomial, a s , is near a polynomial with multiple roots, then small changes in the data, including roundoff errors, can result in arbitrarily large changes in the resulting poles and residues.14