Multivariate Rational Approximation Using a Stabilized Sanathanan-Koerner Iteration

Understand

The Sanathanan-Koerner iteration developed in 1963 is classical approach for rational approximation.

• This approach multiplies both sides of the approximation by the denominator polynomial yielding a linear problem and then introduces a weight at each iteration to correct for this linearization.
• Unfortunately this weight introduces a numerical instability.
• We correct this instability by constructing Vandermonde matrices for both the numerator and denominator polynomials using the Arnoldi iteration with an initial vector that enforces this weighting.