We propose an algorithm to compute the spectral set of a polytope of polynomials. The proposed algorithm offers several key guarantees that are not available with existing techniques. It guarantees that the generated spectral set: (i) contains all the actual points, (ii) is computed to a prescribed accuracy, (iii) is computed reliably in face of all kinds of computational errors, and (iv) is computed in a finite number of algorithmic iterations. A further merit is that the computational complexity of the proposed algorithm is in contrast to for existing techniques, where is the degree of the polynomial. The algorithm is demonstrated on a few examples.
A Reliable Algorithm to Compute the Spectral Set of a Polytope of Polynomials to Prescribed Accuracy
Paluri, N. S. V., and Barve, J. J. (March 28, 2005). "A Reliable Algorithm to Compute the Spectral Set of a Polytope of Polynomials to Prescribed Accuracy." ASME. J. Dyn. Sys., Meas., Control. June 2006; 128(2): 400–405. https://doi.org/10.1115/1.2196416
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