Allowing for the inclusion of the parity operator, it is possible to construct a model of an oscillator whose Hamiltonian admits an exact square root which is rather different from the conventional approach based on creation and annihilation operators. We outline such a model, the method of solution and some generalisations. 03.65.Ge, 03.65.Fd Typeset using REVTEX In memory of Lorella M Jones w...

Use of data assimilation techniques is becoming increasingly common across many application areas. The inverse Hessian (and its square root) plays an important role in several different aspects of these processes. In geophysical and engineering applications, the Hessian-vector product is typically defined by sequential solution of a tangent linear and adjoint problem; for the inverse Hessian, h...

This paper deals with the problem of multi-target tracking in a distributed camera network using the square-root cubature information filter (SCIF). SCIF is an efficient and robust nonlinear filter for multi-sensor data fusion. In camera networks, multiple cameras are arranged in a dispersed manner to cover a large area, and the target may appear in the blind area due to the limited field of vi...

Recently, we proposed an algebraic difference scheme, with extended stability properties, for linear boundary value problems involving stiff differential equations of first order. Here, an efficient approximation scheme is presented for matrix square roots, which provides the stabilization of that scheme in case of stiffness. It combines the use of low-rank matrix approximations from projection...

Let a smooth family of Riemannian metrics g(τ) satisfy the backwards Ricci flow equation on a compact oriented n-dimensional manifold M . Suppose two families of normalized n-forms ω(τ) ≥ 0 and ω̃(τ) ≥ 0 satisfy the forwards (in τ) heat equation on M generated by the connection Laplacian ∆g(τ). If these n-forms represent two evolving distributions of particles over M , the minimum root-mean-squa...

We discuss the formal verification of some low-level mathematical software for the Intel Itanium architecture. A number of important algorithms have been proven correct using the HOL Light theorem prover. After briefly surveying some of our formal verification work, we discuss in more detail the verification of a square root algorithm, which helps to illustrate why some features of HOL Light,...

Let Sn be the positive real symmetric matrix of order n with (i, j ) entry equal to ( i + j − 2 j − 1 ) , and let x be a positive real number. Eigenvalues of the Hadamard (or entry wise) power S n are considered. In particular for k a positive integer, it is shown that both the Perron root and the trace of S n are approximately equal to 4 4k−1 ( 2n− 2 n− 1 )k . © 2005 Elsevier Inc. All rights r...

Split window (SW) methods, which have been successfully used to retrieve measurements of land surface temperature (LST) and sea surface temperature (SST) from MODIS images, were exploited to evaluate the SST data of three sections of Italian coastal waters. For this purpose, sea surface emissivity (SSE) values were estimated by adding the effects of salinity and total suspended particulate matt...

in this paper we study the concept of latin-majorizati-on. geometrically this concept is different from other kinds of majorization in some aspects. since the set of all $x$s latin-majorized by a fixed $y$ is not convex, but, consists of :union: of finitely many convex sets. next, we hint to linear preservers of latin-majorization on $ mathbb{r}^{n}$ and ${m_{n,m}}$.