10 research outputs found
LSMR Iterative Method for General Coupled Matrix Equations
By extending the idea of LSMR method, we present an iterative method to solve the general coupled matrix equations ∑k=1qAikXkBik=Ci, i=1,2,…,p, (including the generalized (coupled) Lyapunov and Sylvester matrix equations as special cases) over some constrained matrix groups (X1,X2,…,Xq), such as symmetric, generalized bisymmetric, and (R,S)-symmetric matrix groups. By this iterative method, for any initial matrix group (X1(0),X2(0),…,Xq(0)), a solution group (X1*,X2*,…,Xq*) can be obtained within finite iteration steps in absence of round-off errors, and the minimum Frobenius norm solution or the minimum Frobenius norm least-squares solution group can be derived when an appropriate initial iterative matrix group is chosen. In addition, the optimal approximation solution group to a given matrix group (X¯1,X¯2,…,X¯q) in the Frobenius norm can be obtained by finding the least Frobenius norm solution group of new general coupled matrix equations. Finally, numerical examples are given to illustrate the effectiveness of the presented method
Analytic families of quantum hyperbolic invariants
We organize the quantum hyperbolic invariants (QHI) of -manifolds into
sequences of rational functions indexed by the odd integers and
defined on moduli spaces of geometric structures refining the character
varieties. In the case of one-cusped hyperbolic -manifolds we generalize
the QHI and get rational functions depending on a
finite set of cohomological data called {\it weights}. These
functions are regular on a determined Abelian covering of degree of a
Zariski open subset, canonically associated to , of the geometric component
of the variety of augmented -characters of . New
combinatorial ingredients are a weak version of branchings which exists on
every triangulation, and state sums over weakly branched triangulations,
including a sign correction which eventually fixes the sign ambiguity of the
QHI. We describe in detail the invariants of three cusped manifolds, and
present the results of numerical computations showing that the functions
depend on the weights as ,
and recover the volume for some specific choices of the weights.Comment: 54 pages, 21 figures. New section with 3 examples; the results about
the reduced invariants are postponed to a separate paper. To appear on Alg.
Geom. Topo
Goddard Laboratory for Atmospheric Sciences, collected reprints 1978 - 1979, volume 2
Information about the Earth hydrosphere, obtained in the field and from aircraft and satellite imagery is reported. Particular emphasis is given to the use of microwave sensors in the study of soil moisture, sea ice, snow cover and atmospheric parameters associated with watersheds
Generalized averaged Gaussian quadrature and applications
A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal
MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications
Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described