Definition 1.1. A weak factorization system (L,R) in a category K consists of two classes L and R of morphisms of K such that (1) R = L , L = R and (2) any morphism h of K has a factorization h = gf with f ∈ L and g ∈ R. Definition 1.2. A model category is a complete and cocomplete category K together with three classes of morphisms F , C and W called fibrations, cofibrations and weak equivalen...

The spectral factorization problem of a scalar coercive spectral density is considered in the framework of the CallierDesoer algebra of distributed parameter system transfer functions. Criteria for the infinite product representation of a coercive spectral density and for the convergence of infinite product representations of spectral factors, i.e. for the convergence of the symmetric extractio...

Let H be a Krull monoid with class group G and suppose that each class contains a prime divisor. Then every element a ∈ H has a factorization into irreducible elements, and the set L(a) of all possible factorization lengths for a is the set of lengths of a. We consider the system L(H) = {L(a) | a ∈ H} of all sets of lengths, and we characterize (in terms of the class group G) when L(H) is addit...

The application of the finite difference method to approximate the solution of an indefinite elliptic problem produces a linear system whose coefficient matrix is block tridiagonal and symmetric indefinite. Such a linear system can be solved efficiently by a conjugate residual method, particularly when combined with a good preconditioner. We show that specific incomplete block factorization exi...

A numerically reliable state space algorithm is proposed for computing normalized coprime factorizations of periodic descriptor systems. A preprocessing step is used in the algorithm to convert the initial problem for possibly non-causal systems into a simpler problem for causal periodic systems. The main computational ingredient here is the computation of a coprime factorization with causal fa...

Behavior tables are a design formalization intended to support interactive design derivation for hardware and embedded systems. It is a reformulation of the DDD transformation system, bridging behavioral and architectural forms of expression. The tabular representations aid in visualizing design aspects that are subject to interactive refinement and optimization. These ideas are illustrated for...

Network Coordinate (NC) is a scalable and efficient mechanism for Internet distance estimation. IDES is the first matrix factorization based NC system. However it suffers from a significant drawback: high distance estimation error in short links, which degrades practical performance in many Internet applications. To overcome this problem, we propose AIDE, a new accurate Internet distance estima...

We study the innnite horizon quadratic cost minimization problem for a linear time-invariant distributed parameter system with nitely may inputs and outputs. We work in an input/output framework, and reduce the unstable case to the stable case by the use of a right coprime factorization of the impulse response and a preliminary stabilizing feedback. The stable case is then solved through spectr...

Complexity/Cost We stated last time that for a system of n equations in n unknowns (represented by an N × N matrix A), both LU and QR-factorization take time proportional to the cube of n (O(n3)). LU-factorization takes less time by a constant factor of around 2 as n gets large, this constant factor is dwarfed by the third power of the matrix dimension, however. Note that the theoretical “best-...

in this paper‎, ‎we determine the simple groups $g=ab$‎, ‎where $b$ is isomorphic to $l_{3}(4)$ and $a$ isomorphic to an alternating or a symmetric group on $ngeq5$‎, ‎letters‎.