Quasiseparable matrices are a class of rank-structured matrices widely used in numerical linear algebra and of growing interest in computer algebra, with applications in e.g. the linearization of polynomial matrices. Various representation formats exist for these matrices that have rarely been compared.

New algorithms are presented for computing annihilating polynomials of Toeplitz, Hankel, and more generally Toeplitz+Hankel-like matrices over a field. Our approach follows works on Coppersmith's block Wiedemann method with structured projections, which have been recently successfully applied for computing the bivariate resultant. A first baby steps/giant steps approach --directly derived using known techniques on structured matrices-- gives a randomized Monte Carlo algorithm for the minimal polynomial of an (n x n) Toeplitz or Hankel-like matrix of displacement rank α using(Õnw-c(w) Õ c(w)) arithmetic operations, where (w) is the exponent of matrix multiplication and (c(2.373) = 0.523) for the best known value of (w). For generic Toeplitz+Hankel-like matrices a second algorithm computes the characteristic polynomial; in particular, when the displacement rank is considered constant, its cost is (Õn2-1/w). Previous algorithms required (O(n2) operations while the exponents presented here are respectively less than 1.86 and 1.58 with the best known estimate for (w).

The development of sustainable transportation infrastructure for people and goods, using new technology and business models, can prove beneficial or detrimental for mobility, depending on its design and use. The focus of this paper is on the increasing impact new mobility services have on traffic patterns and transportation efficiency in general. Over the last decade, the rise of the mobile internet and the usage of mobile devices have enabled ubiquitous traffic information. With the increased adoption of specific smartphone applications, the number of users of routing applications has become large enough to disrupt traffic flow patterns in a significant manner. Similarly, but at a slightly slower pace, novel services for freight transportation and city logistics improve the efficiency of goods transportation and change the use of road infrastructure. This paper provides a general four-layer framework for modeling these new trends. The main motivation behind the development is to provide a unifying formal system description that can at the same time encompass system physics (flow and motion of vehicles) as well as coordination strategies under various information and cooperation structures. To showcase the framework, we apply it to the specific challenge of modeling and analyzing the integration of routing applications in today's transportation systems. In this framework, at the lowest layer (flow dynamics), we distinguish routed users from nonrouted users. A distributed parameter model based on a nonlocal partial differential equation is introduced and analyzed. The second layer incorporates connected services (e.g., routing) and other applications used to optimize the local performance of the system. As inputs to those applications, we propose a third layer introducing the incentive design and global objectives, which are typically varying over the day depending on road and weather conditions, external events, etc. The high-level planning is handled on the fourth layer taking social longterm objectives into account. We illustrate the framework by considering its ability to model at two different levels. Specific to vehicular traffic, numerical examples enable us to demonstrate the links between the traffic network layer and the routing decision layer. With a second example on optimized freight transport, we then discuss the links between the cooperative control layer and the lower layers. The congestion pricing in Stockholm is used to illustrate how also the social planning layer can be incorporated in future mobility services.