Computing Truncated Joint Approximate Eigenbases for Model Order Reduction
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In this document, some elements of the theory and algorithmics corresponding to the existence and computability of approximate joint eigenpairs for finite collections of matrices with applications to model order reduction, are presented. More specifically, given a finite collection X_1,…,X_d of Hermitian matrices in ℂ^n× n, a positive integer r≪ n, and a collection of complex numbers x̂_j,k∈ℂ for 1≤ j≤ d, 1≤ k≤ r. First, we study the computability of a set of r vectors w_1,…,w_r∈ℂ^n, such that w_k=min_w∈ℂ^n∑_j=1^dX_jw-x̂_j,k w^2 for each 1≤ k ≤ r, then we present a model order reduction procedure based on the truncated joint approximate eigenbases computed with the aforementioned techniques. Some prototypical algorithms together with some numerical examples are presented as well.
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