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1.
Numerical solution of constant coefficient linear delay differential equations as abstract Cauchy problems 总被引:2,自引:0,他引:2
Summary. In this paper we present an approach for the numerical solution of delay differential equations
where , and , different from the classical step-by-step method. We restate (1) as an abstract Cauchy problem and then we discretize it
in a system of ordinary differential equations. The scheme of discretization is proved to be convergent. Moreover the asymptotic
stability is investigated for two significant classes of asymptotically stable problems (1).
Received May 4, 1998 / Revised version received January 25, 1999 / Published online November 17, 1999 相似文献
2.
A. Melman 《Numerische Mathematik》1995,69(4):483-493
Summary.
A method is proposed for the solution of a secular equation, arising
in modified symmetric eigenvalue problems and in several other
areas.
This equation has singularities which make the application of standard root-finding
methods difficult.
In order to solve the equation, a class of transformations of variables is
considered, which transform the equation into one for which Newton's method
converges from any point in a certain given interval. In addition, the form of the
transformed equation suggests a convergence accelerating modification of
Newton's method. The same ideas are applied to the secant
method and numerical results are presented.
Received July 1, 1994 相似文献
3.
Summary. We consider a smoothing-type method for the solution of linear programs. Its main idea is to reformulate the primal-dual
optimality conditions as a nonlinear and nonsmooth system of equations, and to apply a Newton-type method to a smooth approximation
of this nonsmooth system. The method presented here is a predictor-corrector method, and is closely related to some methods
recently proposed by Burke and Xu on the one hand, and by the authors on the other hand. However, here we state stronger global
and/or local convergence properties. Moreover, we present quite promising numerical results for the whole netlib test problem
collection.
Received August 9, 2000 / Revised version received September 28, 2000 / Published online June 7, 2001 相似文献
4.
Summary. In this work, we introduce and analyze two new techniques for obtaining the Q factor in the QR factorization of some (or all) columns of a fundamental solution matrix Y of a linear differential system. These techniques are based on elementary Householder and Givens transformations. We implement
and compare these new techniques with existing approaches on some examples.
Received October 27, 1997 / Revised version received September 21, 1998 / Published online August 19, 1999 相似文献
5.
Ruled Weingarten surfaces in Minkowski 3-space 总被引:1,自引:0,他引:1
We characterize all ruled surfaces in Minkowski 3-space with a relation between the Gauss and mean curvature (Weingarten surfaces).
It turns out that, except if the rulings are in a null direction, these are given by Lorentzian screw motions of straight
lines. However, if the rulings are always in a null direction, then every ruled surface is Weingarten.
Received: 9 February 1998 / Revised version: 20 December 1998 相似文献
6.
Summary.
We construct and analyse a family of absorbing boundary
conditions for diffusion equations with variable coefficients, curved
artifical boundary, and arbitrary convection. It relies on the geometric
identification of the Dirichlet to Neumann map and rational
interpolation of in the complex plane.
The boundary conditions
are stable, accurate, and practical for computations.
Received
December 12, 1992 / Revised version received July 4, 1994 相似文献
7.
8.
We give sharp, necessary conditions on complete embedded CMC surfaces with three ends and an extra reflection symmetry. The respective submoduli space is a two-dimensional variety in the moduli space of general CMC surfaces. Fundamental domains of our CMC surfaces are characterized by associated great circle polygons in the three-sphere. Received: 23 January 1998 / Revised version: 23 October 1998 相似文献
9.
Vicent Caselles Ron Kimmel Guillermo Sapiro Catalina Sbert 《Numerische Mathematik》1997,77(4):423-451
Summary. A novel geometric approach for three dimensional object segmentation is presented. The scheme is based on geometric deformable
surfaces moving towards the objects to be detected. We show that this model is related to the computation of surfaces of minimal
area (local minimal surfaces). The space where these surfaces are computed is induced from the three dimensional image in
which the objects are to be detected. The general approach also shows the relation between classical deformable surfaces obtained
via energy minimization and geometric ones derived from curvature flows in the surface evolution framework. The scheme is
stable, robust, and automatically handles changes in the surface topology during the deformation. Results related to existence,
uniqueness, stability, and correctness of the solution to this geometric deformable model are presented as well. Based on
an efficient numerical algorithm for surface evolution, we present a number of examples of object detection in real and synthetic
images.
Received January 4, 1996 / Revised version received August 2, 1996 相似文献
10.
Summary.
We consider the application of linear multistep methods (LMMs)
for the numerical solution of initial value problem for stiff delay
differential equations (DDEs) with several constant delays, which are
used in mathematical modelling of immune response. For the approximation
of delayed variables the Nordsieck's interpolation technique, providing
an interpolation procedure consistent with the underlying linear
multistep formula, is used. An analysis of the convergence for a
variable-stepsize and structure of the asymptotic expansion of global
error for a fixed-stepsize is presented. Some absolute stability
characteristics of the method are examined. Implementation details of
the code DIFSUB-DDE, being a modification of the Gear's DIFSUB, are
given. Finally, an efficiency of the code developed for solution of
stiff DDEs over a wide range of tolerances is illustrated on biomedical
application model.
Received
March 23, 1994 / Revised version received March 13,
1995 相似文献
11.
Summary. This paper presents a new efficient algorithm for solving bidiagonal systems of linear equations on massively parallel machines.
We use a divide and conquer approach to compute a representative subset of the solution components after which we solve the
complete system in parallel with no communication overhead. We address the numerical properties of the algorithm in two ways:
we show how to verify the à posteriori backward stability at virtually no additional cost, and prove that the algorithm is à priori forward stable. We then show how we can use the algorithm in order to bound the possible perturbations in the solution components.
Received March 13, 1998 / Revised version received December 21, 1999 / Published online June 20, 2001 相似文献
12.
ribbon graphs , i.e., graphs realized as disks (vertices) joined together by strips (edges) glued to their boundaries, corresponding to
neighbourhoods of graphs embedded into surfaces. We construct a four-variable polynomial invariant of these objects, the ribbon graph polynomial, which has all the main properties of the Tutte polynomial. Although the ribbon graph polynomial extends the Tutte polynomial,
its definition is very different, and it depends on the topological structure in an essential way.
Received: 14 September 2000 / Published online: 18 January 2002 相似文献
13.
Joaquín Pérez 《Mathematische Annalen》1998,310(2):307-332
14.
Summary. Solutions of symmetric Riccati differential equations (RDEs for short) are in the usual applications positive semidefinite
matrices. Moreover, in the class of semidefinite matrices, solutions of different RDEs are also monotone, with respect to
properly ordered data. Positivity and monotonicity are essential properties of RDEs. In Dieci and Eirola (1994), we showed
that, generally, a direct discretization of the RDE cannot maintain positivity, and be of order greater than one. To get higher
order, and to maintain positivity, we are thus forced to look into indirect solution procedures. Here, we consider the problem
of how to maintain monotonicity in the numerical solutions of RDEs. Naturally, to obtain order greater than one, we are again
forced to look into indirect solution procedures. Still, the restrictions imposed by monotonicity are more stringent that
those of positivity, and not all of the successful indirect solution procedures of Dieci and Eirola (1994) maintain monotonicity.
We prove that by using symplectic Runge-Kutta (RK) schemes with positive weights (e.g., Gauss schemes) on the underlying Hamiltonian
matrix, we eventually maintain monotonicity in the computed solutions of RDEs.
Received May 2, 1995 相似文献
15.
Summary. It is well known that any nonsingular M–matrix admits an LU factorization into M–matrices (with L and U lower and upper triangular respectively) and any singular M–matrix is permutation similar to an M–matrix which admits an
LU factorization into M–matrices. Varga and Cai establish necessary and sufficient conditions for a singular M–matrix (without
permutation) to allow an LU factorization with L nonsingular. We generalize these results in two directions. First, we find necessary and sufficient conditions for the existence
of an LU factorization of a singular M-matrix where L and U are both permitted to be singular. Second, we establish the minimal block structure that a block LU factorization of a singular
M–matrix can have when L and U are M–matrices.
Received November 21, 1994 / Revised version received August 4, 1997 相似文献
16.
In this paper we give a conformal representation of flat surfaces in the hyperbolic 3-space using the complex structure induced
by its second fundamental form. We also study some examples and the behaviour at infinity of complete flat ends.
Received: 18 September 1997 相似文献
17.
Summary.
The existence of a true orbit near a numerically
computed approximate orbit -- shadowing -- of
autonomous system of ordinary differential equations
is investigated.
A general shadowing theorem for finite time,
which guarantees the existence of shadowing
in ordinary differential equations
and provides error bounds for the distance between
the true and the approximate orbit in terms of computable
quantities, is proved.
The practical use and the effectiveness of this theorem
is demonstrated in the numerical computations
of chaotic orbits of the Lorenz equations.
Received December 15, 1993 相似文献
18.
Summary. Interpolation with translates of a basis function is a common process in approximation theory. The most elementary form of
the interpolant consists of a linear combination of all translates by interpolation points of a single basis function. Frequently,
low degree polynomials are added to the interpolant. One of the significant features of this type of interpolant is that it
is often the solution of a variational problem. In this paper we concentrate on developing a wide variety of spaces for which
a variational theory is available. For each of these spaces, we show that there is a natural choice of basis function. We
also show how the theory leads to efficient ways of calculating the interpolant and to new error estimates.
Received December 10, 1996 / Revised version received August 29, 1997 相似文献
19.
G.W. Stewart 《Numerische Mathematik》1994,68(1):143-147
Summary.
This note gives a new convergence proof for iterations based on
multipoint formulas. It rests on the very general assumption that if
the desired fixed point appears as an argument in the formula then
the formula returns the fixed point.
Received March 24, 1993 / Revised version received
January 1994 相似文献
20.
Summary. We present a new class of integration methods for differential equations on manifolds, in the framework of Lie group actions.
Canonical coordinates of the second kind is used for representing the Lie group locally by means of its corresponding Lie
algebra. The coordinate map itself can, in many cases, be computed inexpensively, but the approach also involves the inversion
of its differential, a task that can be challenging. To succeed, it is necessary to consider carefully how to choose a basis
for the Lie algebra, and the ordering of the basis is important as well. For semisimple Lie algebras, one may take advantage
of the root space decomposition to provide a basis with desirable properties. The problem of ordering leads us to introduce
the concept of an admissible ordered basis (AOB). The existence of an AOB is established for some of the most important Lie
algebras. The computational cost analysis shows that the approach may lead to more efficient solvers for ODEs on manifolds
than those based on canonical coordinates of the first kind presented by Munthe-Kaas. Numerical experiments verify the derived
properties of the new methods.
Received April 2, 1999 / Revised version received January 18, 2000 / Published online August 2, 2000 相似文献