8 citations · 12 across the 10 of their papers we have counts for
10 papers
Geometry in global coordinates in mechanics and optimal transport
Du Nguyen
For a manifold embedded in an inner product space, we express geometric quantities such as {\it Hamilton vector fields, affine and Levi-Civita connections, curvature} in global coo…
Curvatures of Stiefel manifolds with deformation metrics
Du Nguyen
We compute curvatures of a family of tractable metrics on Stiefel manifolds, introduced recently by H{ü}per, Markina and Silva Leite, which includes the well-known embedded and can…
Riemannian Geometry with differentiable ambient space and metric operator
Du Nguyen
We show Riemannian geometry could be studied by identifying the tangent bundle of a Riemannian manifold with a subbundle of the trivial bundle $\mathcal{M} \times \ma…
Closed-form geodesics and trust-region method to calculate Riemannian logarithms on Stiefel and its quotient manifolds
Du Nguyen
We provide two closed-form geodesic formulas for a family of metrics on Stiefel manifold, parameterized by two positive numbers, having both the embedded and canonical metrics as s…
Riemannian gradient and Levi-Civita connection for fixed-rank matrices
Du Nguyen
We provide formulas for Riemannian gradient and Levi-Civita connection for a family of metrics on fixed-rank matrix manifolds, based on nonconstant metrics on Stiefel manifolds.
Operator-valued formulas for Riemannian Gradient and Hessian and families of tractable metrics
Du Nguyen
We provide an explicit formula for the Levi-Civita connection and Riemannian Hessian for a Riemannian manifold that is a quotient of a manifold embedded in an inner product space w…
A theorem of Kalman and minimal state-space realization of Vector Autoregressive Models
Du Nguyen
We introduce a concept of (AR)state-space realization that could be applied to all transfer functions with invertible. We s…
Vector Autoregressive Moving Average Model with Scalar Moving Average
Du Nguyen
We show Vector Autoregressive Moving Average models with scalar Moving Average components could be estimated by generalized least square (GLS) for each fixed moving average polynom…
Rayleigh Quotient Iteration, cubic convergence, and second covariant derivative
Du Nguyen
We generalize the Rayleigh Quotient Iteration (RQI) to the problem of solving a nonlinear equation where the variables are divided into two subsets, one satisfying additional equal…
An Explicit Formula for Likelihood Function for Gaussian Vector Autoregressive Moving-Average Model Conditioned on Initial Observables with Application to Model Calibration
Du Nguyen
We derive an explicit formula for likelihood function for Gaussian VARMA model conditioned on initial observables where the moving-average (MA) coefficients are scalar. For fixed M…