Topics include matrix calculus for finite and infinite matrices (e.g., Wigner's semi-circle and Marcenko-Pastur laws), free probability, random graphs, combinatorial methods, matrix statistics, stochastic operators, passage to the continuum limit, moment methods, and compressed sensing.
It turns out that computing the exponential of strictly elliptic operators in the wavelet system of coordinates yields sparse matrices (for a finite but arbitrary accuracy).
We numerically investigated the conditioning of the stiffness matrices for the finite element approximations of the two formulations of the Nernst Planck equation, and theoretically proved that the transformed formulation is always associated with an ill-conditioned stiffness matrix.
A GP is defined by a mean function and a covariance function, which specify the mean vectors and covariance matrices for each finite collection of the random variables.
However, two barriers are encountered when using matrix groups for finite motion composition in formulating topological models.
We conclude that the paraxial approximation offers an efficient method for computing the matrix system for finite-frequency inversions in global tomography, though care should be taken near reflection points, and alternative methods are needed to compute sensitivity near the antipode.
Even though freeness usually does not hold for finite matrices, the moments method can still be used to propose algorithmic methods to compute their moments.
Our results imply various abstract variants of Schurʼs classical result, and in particular we extend Pisierʼs converse for matrices in finite dimensional ℓp-spaces to the setting of complex Calderón interpolation of finite dimensional Banach lattices.
In the following, we will show that the number of distinct difference indicator matrices is finite for bounded N, and that the sequence of difference indicator matrices {Δ t′} is stationary Markov and ergodic.
We establish the non-self-adjoint analogs of the Hochstadt and Gesztesy Simon uniqueness theorems for finite Jacobi matrices with nonreal eigenvalues as well as an extension and refinement of these theorems for finite non-self-adjoint tri-diagonal matrices to the case of mixed eigenvalues, real and nonreal.
