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Hierarchical matrices (
-matrices) approximate matrices in a data-sparse way, and the approximate arithmetic for
-matrices is almost optimal. In this paper we present an algebraic approach for constructing
-matrices which combines multilevel clustering methods with
-matrix arithmetic to compute the
-inverse,
-LU, and the
-Cholesky factors of a matrix. Then the
-inverse,
-LU or
-Cholesky factors can be used as preconditioners in iterative methods to solve systems of linear equations. The numerical
results show that this method is efficient and greatly speeds up convergence compared to other approaches, such as JOR or
AMG, for solving some large, sparse linear systems, and is comparable to other
-matrix constructions based on Nested Dissection. 相似文献
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Eric Allender Anna Bernasconi Carsten Damm Joachim von zur Gathen Michael Saks Igor Shparlinski 《Computational Complexity》2003,12(1-2):23-47
We study various combinatorial complexity measures of
Boolean functions related to some natural arithmetic problems about
binary polynomials, that is, polynomials over
.
In particular, we consider
the Boolean function deciding whether a given polynomial over
is squarefree. We obtain an exponential lower bound on the size of a
decision tree for this function, and derive an asymptotic formula, having
a linear main term, for its average sensitivity. This allows us to estimate
other complexity characteristics such as the formula size, the average decision
tree depth and the degrees of exact and approximative polynomial
representations of this function. Finally, using a different method, we
show that testing squarefreeness and irreducibility of polynomials over
cannot be done in
for any odd prime p. Similar results are
obtained for deciding coprimality of two polynomials over
as well. 相似文献
6.
Emanuele Viola 《Computational Complexity》2005,13(3-4):147-188
We study the complexity of constructing pseudorandom generators (PRGs) from hard functions, focussing on constant-depth circuits. We show that, starting from a function
computable in alternating time O(l) with O(1) alternations that is hard on average (i.e. there is a constant
such that every circuit of size
fails to compute f on at least a 1/poly(l) fraction of inputs) we can construct a
computable by DLOGTIME-uniform constant-depth circuits of size polynomial in n. Such a PRG implies
under DLOGTIME-uniformity. On the negative side, we prove that starting from a worst-case hard function
(i.e. there is a constant
such that every circuit of size
fails to compute f on some input) for every positive constant
there is no black-box construction of a
computable by constant-depth circuits of size polynomial in n. We also study worst-case hardness amplification, which is the related problem of producing an average-case hard function starting from a worst-case hard one. In particular, we deduce that there is no blackbox worst-case hardness amplification within the polynomial time hierarchy. These negative results are obtained by showing that polynomialsize constant-depth circuits cannot compute good extractors and listdecodable codes. 相似文献
7.
Any given n×n matrix A is shown to be a restriction, to the A-invariant subspace, of a nonnegative N×N matrix B of spectral radius (B) arbitrarily close to (A). A difference inclusion
, where
is a compact set of matrices, is asymptotically stable if and only if
can be extended to a set
of nonnegative matrices B with
or
. Similar results are derived for differential inclusions. 相似文献
8.
On Defining Integers And Proving Arithmetic Circuit Lower Bounds 总被引:1,自引:1,他引:0
Peter Bürgisser 《Computational Complexity》2009,18(1):81-103
9.
Remco Duits Michael Felsberg Gösta Granlund Bart ter Haar Romeny 《International Journal of Computer Vision》2007,72(1):79-102
Inspired by the early visual system of many mammalians we consider the construction of-and reconstruction from- an orientation
score
as a local orientation representation of an image,
. The mapping
is a wavelet transform
corresponding to a reducible representation of the Euclidean motion group onto
and oriented wavelet
. This wavelet transform is a special case of a recently developed generalization of the standard wavelet theory and has the
practical advantage over the usual wavelet approaches in image analysis (constructed by irreducible representations of the
similitude group) that it allows a stable reconstruction from one (single scale) orientation score. Since our wavelet transform
is a unitary mapping with stable inverse, we directly relate operations on orientation scores to operations on images in a
robust manner.
Furthermore, by geometrical examination of the Euclidean motion group
, which is the domain of our orientation scores, we deduce that an operator Φ on orientation scores must be left invariant
to ensure that the corresponding operator
on images is Euclidean invariant. As an example we consider all linear second order left invariant evolutions on orientation
scores corresponding to stochastic processes on G. As an application we detect elongated structures in (medical) images and automatically close the gaps between them.
Finally, we consider robust orientation estimates by means of channel representations, where we combine robust orientation
estimation and learning of wavelets resulting in an auto-associative processing of orientation features. Here linear averaging
of the channel representation is equivalent to robust orientation estimation and an adaptation of the wavelet to the statistics
of the considered image class leads to an auto-associative behavior of the system.
The Netherlands Organization for Scientific Research is gratefully acknowledged for financial support. This work has been
supported by EC Grant IST-2003-004176 COSPAL. 相似文献
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Escape analysis of object-oriented languages approximates the set of objects which do not escape from a given context. If we take a method as context, the non-escaping objects can be allocated on its activation stack;
if we take a thread, Java synchronisation locks on such objects are not needed. In this paper, we formalise a basic escape
domain
as an abstract interpretation of concrete states, which we then refine into an abstract domain
which is more concrete than
and, hence, leads to a more precise escape analysis than
. We provide optimality results for both
and
, in the form of Galois insertions from the concrete to the abstract domains and of optimal abstract operations. The Galois
insertion property is obtained by restricting the abstract domains to those elements which do not contain garbage, by using an abstract garbage collector. Our implementation of
is hence an implementation of a formally correct escape analyser, able to detect the stack allocatable creation points of
Java (bytecode) applications. 相似文献
12.
In this paper we deal with the problem of controlling a safe place/transition net so as to avoid a set of forbidden markings
. We say that a given set of markings has property REACH if it is closed under the reachability operator. We assume that all
transitions of the net are controllable and that the set of forbidden markings
has the property REACH.
The technique of unfolding is used to design a maximally permissive supervisor to solve this control problem. The supervisor
takes the form of a set of control places to be added to the unfolding of the original net.
The approach is also extended to the problem of preventing a larger set
of impending forbidden marking. This is a superset of the forbidden markings that also includes all those markings from which—unless
the supervisor blocks the plant—a marking in
is inevitably reached in a finite number of steps.
Finally, we consider the particular case in which the control objective is that of designing a maximally permissive supervisor
for deadlock avoidance and we show that in this particular case our procedure can be efficiently implemented by means of linear
algebraic techniques.
Submitted to Discrete Event Dynamic Systems. A preliminary version of this paper titled “Control of safe ordinary Petri nets with marking specifications using unfolding,”
was published in the Proc. IFAC WODES'04: 7th Work. on Discrete Event Systems (Reims, France), September 2004. Contact author is Alessandro Giua. 相似文献
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Agent Communication Languages (ACLs) have been developed to provide a way for agents to communicate with each other supporting
cooperation in Multi-Agent Systems (MAS). In the past few years many ACLs have been proposed for MAS and new standards are
emerging such as the ACL developed by the Foundation for Intelligent Physical Agents (FIPA). Despite these efforts, an important
issue in the research on ACLs is still open and concerns how these languages should deal with failures of agents in asynchronous MAS. The Fault Tolerant Agent Communication Language (
-
) presented in this paper addresses this issue dealing with crash failures of agents.
-
provides high-level communication primitives which support a fault-tolerant anonymous interaction protocol designed for open
MAS. We present a formal semantics for
-
and a formal specification of the underlying agent architecture. This formal framework allows us to prove that the ACL satisfies
a set of well defined knowledge-level programming requirements. To illustrate the language features we show how
-
can be effectively used to write high-level executable specifications of fault tolerant protocols, such as the Contract Net
one. 相似文献
15.
R. F. Streater 《Open Systems & Information Dynamics》2004,11(4):359-375
Let H0 be a selfadjoint operator such that Tr
is of trace class for some
, and let
denote the set of ε-bounded forms, i.e.,
for some
0 $$" align="middle" border="0">
. Let χ := Span
. Let
denote the underlying set of the quantum information manifold of states of the form
. We show that if Tr
,
Presented at the 36th Symposium on Mathematical Physics, ‘Open Systems & Quantum Information’, Toruń, Poland, June 9-12, 2004. 相似文献
1. | the map Φ,
| |
2. | The Orlicz space defined by Φ is the tangent space of at ρ0; its affine structure is defined by the (+1)-connection of Amari | |
3. | The subset of a ‘hood of ρ0, consisting of p-nearby states (those obeying for some 1$$" align="middle" border="0"> ) admits a flat affine connection known as the (-1) connection, and the span of this set is part of the cotangent space of | |
4. | These dual structures extend to the completions in the Luxemburg norms. |
16.
We construct a linear interval system Ax = b with a 4 × 4 interval matrix whose all proper interval coefficients (there are also some noninterval ones) are of the form [–, ]. It is proved that for each > 0, the interval hull
and interval hull of the midpoint preconditioned system
satisfy
and
, hence midpoint preconditioning produces a 100% overestimation of
independently of in this case. The example was obtained as a result of an extensive MATLAB search. 相似文献
17.
Every Linear Threshold Function has a Low-Weight Approximator 总被引:1,自引:1,他引:0
Rocco A. Servedio 《Computational Complexity》2007,16(2):180-209
18.
Let
be a finite field withq elements and
a rational function over
. No polynomial-time deterministic algorithm is known for the problem of deciding whetherf induces a permutation on
. The problem has been shown to be in co-R
co-NP, and in this paper we prove that it is inR
NP and hence inZPP, and it is deterministic polynomial-time reducible to the problem of factoring univariate polynomials over
. Besides the problem of recognizing prime numbers, it seems to be the only natural decision problem inZPP unknown to be inP. A deterministic test and a simple probabilistic test for permutation functions are also presented. 相似文献
19.
Abstract We obtain a multivariate extension of a classical result of Schoenberg on cardinal spline interpolation. Specifically, we
prove the existence of a unique function in
, polyharmonic of order p on each strip
,
, and periodic in its last n variables, whose restriction to the parallel hyperplanes
,
, coincides with a prescribed sequence of n-variate periodic data functions satisfying a growth condition in
. The constructive proof is based on separation of variables and on Micchelli’s theory of univariate cardinal
-splines.
Keywords: cardinal
-splines, polyharmonic functions, multivariable interpolation
Mathematics Subject Classification (2000): 41A05, 41A15, 41A63 相似文献
20.
I. V. Gaishun 《Automation and Remote Control》2002,63(11):1717-1723
A class of two-parameter discrete systems defined on the ring
of class of residues of integers
modulo m is studied. All solutions are shown to be periodic, stability conditions (equality of solutions to zero, beginning from a certain instant) and a controllability condition are formulated. Controllability is shown to guarantee stabilizability. 相似文献