Papers › Computing Truncated Joint Approximate Eigenbases for Model Order Reduction
Computing Truncated Joint Approximate Eigenbases for Model Order Reduction
Terry A. Loring, Fredy Vides
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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 X₁,…,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 w₁,…,wᵣ∈ℂⁿ, such that wₖ=min_(w∈ℂⁿ)∑ⱼ₌₁ᵈXⱼw-x̂_(j,k) w² 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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