The Mahalanobis Taguchi System (MTS) is a diagnosis and forecasting method for multivariate data. Mahalanobis distance (MD) is a measure based on correlations between the variables and different patterns that can be identified and analyzed with respect to a base or reference group. MTS is of interest because of its reported accuracy in forecasting small, correlated data sets. This is the type o...

Gradient-based optimisation relies on the response Jacobian whose evaluation constitutes a major computational overhead in full-wave numerical analysis. Adjoint-based techniques may offer numerically efficient solutions, but their implementation is too involved in the case of fullwave computations. A simple approach that uses the self-adjoint sensitivity analysis and Broyden’s update is propose...

Continuity properties of factors in polar decompositions of matrices with respect to inde®nite scalar products are studied. The matrix having the polar decomposition and the inde®nite scalar product are allowed to vary. Closely related properties of a self-adjoint (with respect to an inde®nite scalar product) perturbed matrix to have a self-adjoint square root, or to have a representation of th...

It is widely appreciated that the iterative solution of linear systems of equations with large sparse matrices is much easier when the matrix is symmetric. It is equally advantageous to employ symmetric iterative methods when a nonsymmetric matrix is self-adjoint in a non-standard inner product. Here, general conditions for such self-adjointness are considered. In particular, a number of known ...

We provide a comparative treatment of some aspects of spectral theory for self-adjoint and non-self-adjoint (but J-self-adjoint) Dirac-type operators connected with the defocusing and focusing nonlinear Schrödinger equation, of relevance to nonlinear optics. In addition to a study of Dirac and Hamiltonian systems, we also introduce the concept of Weyl–Titchmarsh half-line m-coefficients (and 2 ...

We continue the study of matrices over a supertropical algebra, proving the existence of a tangible adjoint of A, which provides the unique right (resp. left) quasi-inverse maximal with respect to the right (resp. left) quasi-identity matrix corresponding to A; this provides a unique maximal (tangible) solution to supertropical vector equations, via a version of Cramer’s rule. We also describe ...

A probabilistic representation for a class of weighted p-radial distributions, based on mixtures cone probability measure and uniform distribution the Euclidean ℓpn-ball, is derived. Large deviation principles empirical coordinates random vectors ℓpn-ball with from this are discussed. The distributions extended to p-balls in classical matrix spaces, both self-adjoint non-self-adjoint matrices. ...