This work presents a parametrized family of divergences, namely Alpha-Beta LogDeterminant (Log-Det) divergences, between positive definite unitized trace class operators on a Hilbert space. This is a generalization of the Alpha-Beta Log-Determinant divergences between symmetric, positive definite matrices to the infinite-dimensional setting. The family of Alpha-Beta Log-Det divergences is highl...

1 I n t r o d u c t i o n . This work appl ies some l inear a lgebra ideas in an o rd ina ry differential equa t ion (ODE) context . We begin by summar i s ing the a p p r o p r i a t e l inear a lgebra , and then we in t roduce the O D E problem. *Received July 1995. Revised July 1996. tThis work was supported by Engineering and Physical Sciences Research Council grants GR/H94634 and GR/KS0228...

In this paper, we describe block matrix algorithms for the iterative solution of large scale linear-quadratic optimal control problems arising from the optimal control of parabolic partial differential equations over a finite control horizon. We describe three iterative algorithms. The first algorithm employs a CG method for solving a symmetric positive definite reduced linear system involving ...

Motivated by statistical challenges arising in modern scientific fields, notably genomics, this paper seeks embeddings which relevant covariance models are sparse. The work exploits a bijective mapping between strictly positive definite matrix and its orthonormal eigen-decomposition, an eigenvector principle logarithm. This leads to representation of matrices terms skew-symmetric matrices, for ...

In this paper, we propose a variationally consistent technique for decreasing the maximum eigenfrequencies of structural dynamics related finite element formulations. Our approach is based on adding symmetric positive-definite term to mass matrix that follows from integral traction jump across boundaries. The added weighted by small factor, which derive suitable, and simple, element-local param...

A class of symmetric static output feedback controllers are known to robustly stabilize symmetric collocated second-order linear time invariant systems having positive definite or positive semi-definite coefficient matrices. This paper extends the result to the asymmetric systems which include skew-symmetric gyroscopic terms. We first obtain the condition for static output feedback controllers ...

In this paper‎, ‎we study convergence behavior of the global FOM (Gl-FOM) and global GMRES (Gl-GMRES) methods for solving the matrix equation $AXB=C$ where $A$ and $B$ are symmetric positive definite (SPD)‎. ‎We present some new theoretical results of these methods such as computable exact expressions and upper bounds for the norm of the error and residual‎. ‎In particular‎, ‎the obtained upper...

Given a symmetric positive definite matrix A, we compute a structured approximate Cholesky factorization A ≈ RTR up to any desired accuracy, where R is an upper triangular hierarchically semiseparable (HSS) matrix. The factorization is stable, robust, and efficient. The method compresses off-diagonal blocks with rank-revealing orthogonal decompositions. In the meantime, positive semidefinite te...

Abstract We use the geometric mean to parametrize metrics in Hassan–Rosen ghost-free bimetric theory and pose initial-value problem. The of two positive definite symmetric matrices is a well-established mathematical notion which can be under certain conditions extended quadratic forms having Lorentzian signature, say g f . In such case, null cone metric h middle cones appearing as average space...