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161.
We give two optimal linear-time algorithms for computing the Longest Previous Factor (LPF) array corresponding to a string w. For any position i in w, LPF[i] gives the length of the longest factor of w starting at position i that occurs previously in w. Several properties and applications of LPF are investigated. They include computing the Lempel-Ziv factorization of a string and detecting all repetitions (runs) in a string in linear time independently of the integer alphabet size. 相似文献
162.
In this paper, we address the identification problem of p-inputs q-outputs MA models, corrupted by a white noise with unknown covariance matrix, in the case where p<q. Under certain additional conditions, we show that the generating function of the MA model is identifiable (up to a p×p constant orthogonal matrix) from the autocovariance function of the observation. Our results extend those already obtained in Desbouvries et al. [5] and Desbouvries and Loubaton [6]. 相似文献
163.
Ruth F. Curtain 《Mathematics of Control, Signals, and Systems (MCSS)》2001,14(4):299-337
We consider the question of the existence of solutions to certain linear operator inequalities (Lur'e equations) for strongly
stable, weakly regular linear systems with generating operators A, B, C, 0. These operator inequalities are related to the spectral factorization of an associated Popov function and to singular
optimal control problems with a nonnegative definite quadratic cost functional. We split our problem into two subproblems:
the existence of spectral factors of the nonnegative Popov function and the existence of a certain extended output map. Sufficient
conditions for the solvability of the first problem are known and for the case that A has compact resolvent and its eigenvectors form a Riesz basis for the state space, we give an explicit solution to the second
problem in terms of A, B, C and the spectral factor. The applicability of these results is demonstrated by various heat equation examples satisfying
a positive-real condition. If (A, B) is approximately controllable, we obtain an alternative criterion for the existence of an extended output operator which
is applicable to retarded systems. The above results have been used to design adaptive observers for positive-real infinite-dimensional
systems.
Date received: July 25, 1997. Date revised: February 10, 2001. 相似文献
164.
We find the following necessary and sufficient conditions for Q (:=C(I+PC)−1) to
-stabilize the standard linear time-invariant unity feedback system S(P, C) where P has the l.c.f. (Dpl, Npl) and the r.c.f. (Npr, Dpr); and
is a principal ideal domain. (i) Q must have elements in
(ii) (resp. (iii)) Q must factorize in
with Dpr, (resp. Dpl) as a left (resp. right) factor and (iv) (I – QP) must factor in
with Dpr, as a left factor. 相似文献
165.
Collaborative filtering (CF) is a data analysis task appearing in many challenging applications, in particular data mining in Internet and e-commerce. CF can often be formulated as identifying patterns in a large and mostly empty rating matrix. In this paper, we focus on predicting unobserved ratings. This task is often a part of a recommendation procedure. We propose a new CF approach called interlaced generalized linear models (GLM); it is based on a factorization of the rating matrix and uses probabilistic modeling to represent uncertainty in the ratings. The advantage of this approach is that different configurations, encoding different intuitions about the rating process can easily be tested while keeping the same learning procedure. The GLM formulation is the keystone to derive an efficient learning procedure, applicable to large datasets. We illustrate the technique on three public domain datasets. 相似文献
166.
In this paper, we present a way of expressing massively parallel algorithms associated with a programming environment for networks of processors with local memory; the aim is to provide a programming method that is independent of the network topology, and that leads to an efficient implementation for communications.
Then, we illustrate these concepts using as an example a scientific algorithm: Choleski's method for a parallel factorization of sparse matrices into blocks.
This work gives rise to software for a T.Node multiprocessor computer. 相似文献
167.
In this paper we show that the separable decomposition of a univariate polynomial can be computed in softly optimal time,
in terms of the number of arithmetic operations in the coefficient field. We also adapt the classical multi-modular strategy
that speeds up the computations for many coefficient fields, and we analyze consequences of the new results to the squarefree
and the irreducible factorizations.
This work was partly supported by the French Research Agency via the Gecko project (gecko.inria.fr). 相似文献
168.
169.
Alan George Michael T. Heath Joseph Liu Esmond Ng 《International journal of parallel programming》1986,15(4):309-325
Algorithms and software for solving sparse symmetric positive definite systems on serial computers have reached a high state of development. In this paper, we present algorithms for performing sparse Cholesky factorization and sparse triangular solutions on a shared-memory multiprocessor computer, along with some numerical experiments demonstrating their performance on a Sequent Balance 8000 system.Research was supported by the Applied Mathematical Sciences Research Program of the Office of Energy Research, U.S. Department of Energy under contract DE-AC05-84OR21400 with Martin Marieta Energy Systems, Inc., by the U.S. Air Force Office of Scientific Research under contract AFOSR-ISSA-85-00083 and by the Canadian Natural Sciences and Engineering Research Council under grants A8111 and A5509. 相似文献
170.
Given a process y with stationary increments and rational incremental spectral density Φ(s), we parametrize minimal state-space representations of dy. We consider the case when Φ(s) may have zeros on the imaginary axis including infinity and we analyze the zero structure of each state-space representation. 相似文献