Numerical operations among rational matrices: Standard techniques and interpolation

Numerical operations on and among rational matrices are traditionally handl ed by direct manipulation with their scalar entries. A new numerically attr active alternative is proposed here that is based on rational matrix interp olation. The procedure begins with evaluation of rational matrices in sever al complex points. Then all the required operations are performed consecuti vely on constant matrices corresponding to each particular point. Finally, the resulting rational matrix is recovered from the particular constant sol utions via interpolation. It may be computed either in polynomial matrix fr action form or as matrix of rational functions. The operations considered i nclude addition, multiplication and computation of polynomial matrix fracti on form. The standard and interpolation methods are compared by experiments .