We present an algorithm for clustering multivariate normal distributions based upon the symmetric, Kullback-Leibler divergence. Optimal mean vector and covariance matrix of the centroid normal distribution are derived and a set of Riccati matrix equations is used to find the optimal covariance matrix. The solutions are found iteratively by alternating the intermediate mean and covariance soluti...

Consider the optimal subspace expansion problem for matrix eigenvalue $Ax=\lambda x$: Which vector $w$ in current $\mathcal{V}$, after multiplied by $A$, provides an approximating a desired eigenvector $x$ sense that has smallest angle with expanded $\mathcal{V}_w=\mathcal{V}+{span}\{Aw\}$, i.e., $w_{opt}=\arg\max_{w\in\mathcal{V}}\cos\angle(\mathcal{V}_w,x)$? This is important as many iterativ...

We use a topology optimization method to design 1-3 piezocomposites with optimal performance characteristics for hydrophone applications. The performance characteristics we focus on are the hydrostatic charge coefficient d spd h , the hydrophone figure of merit d spd h g spd h , and the electromechanical coupling factor k spd h . The piezocomposite consists of piezoelectric rods embedded in an ...