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1.
In this paper, some semismooth methods are considered to solve a nonsmooth equation which can arise from a discrete version of the well-known Hamilton-Jacobi-Bellman equation. By using the slant differentiability introduced by Chen, Nashed and Qi in 2000, a semismooth Newton method is proposed. The method is proved to have monotone convergence by suitably choosing the initial iterative point and local superlinear convergence rate. Moreover, an inexact version of the proposed method is introduced, which reduces the cost of computations and still preserves nice convergence properties. Some numerical results are also reported. 相似文献
2.
Some new numerical results for the near-breakdown free version of Lanczos method are reported. 相似文献
3.
QMR: a quasi-minimal residual method for non-Hermitian linear systems 总被引:12,自引:0,他引:12
Summary The biconjugate gradient (BCG) method is the natural generalization of the classical conjugate gradient algorithm for Hermitian positive definite matrices to general non-Hermitian linear systems. Unfortunately, the original BCG algorithm is susceptible to possible breakdowns and numerical instabilities. In this paper, we present a novel BCG-like approach, the quasi-minimal residual (QMR) method, which overcomes the problems of BCG. An implementation of QMR based on a look-ahead version of the nonsymmetric Lanczos algorithm is proposed. It is shown how BCG iterates can be recovered stably from the QMR process. Some further properties of the QMR approach are given and an error bound is presented. Finally, numerical experiments are reported.This work was supported in part by DARPA via Cooperative Agreement NCC 2-387 between NASA and the Universities Space Research Association (USRA). 相似文献
4.
Manabu Sakai 《Numerische Mathematik》1997,76(3):403-417
Summary. This paper considers the distribution of inflection points and singularity on the parametric rational cubic curve, using
much algebraic manipulation. Its use allows one to find a shape preserving interpolatory rational cubic curve of a planar
data. Some numerical examples are given to illustrate usefulness of the method.
Received April 30, 1995 / Revised version received January 15, 1996 相似文献
5.
C.V. Pao 《Numerische Mathematik》1998,79(2):261-281
This paper is concerned with numerical methods for a finite difference system of reaction-diffusion-convection equation under
nonlinear boundary condition. Various monotone iterative methods are presented, and each of these methods leads to an existence-comparison
theorem as well as a computational algorithm for numerical solutions. The monotone property of the iterations gives improved
upper and lower bounds of the solution in each iteration, and the rate of convergence of the iterations is either quadratic
or nearly quadratic depending on the property of the nonlinear function. Application is given to a model problem from chemical
engineering, and some numerical results, including a test problem with known analytical solution, are presented to illustrate
the various rates of convergence of the iterations.
Received November 2, 1995 / Revised version received February 10, 1997 相似文献
6.
We study numerical solution branches of certain parameter-dependent problems defined on compact domains with various boundary
conditions. The finite differences combined with the domain decomposition method are exploited to discretize the partial differential
equations. We propose efficient numerical algorithms for solving the associated linear systems and for the detection of bifurcation
points. Sample numerical results are reported.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
7.
Summary.
Maximum entropy density estimation, a technique for
reconstructing an unknown density function on the basis
of certain measurements, has applications in various
areas of applied physical sciences and engineering. Here
we present numerical results for the maximum entropy inversion
program based on a new class of information measures which
are designed to control derivative values of the unknown
densities.
Received January 3, 1994 /
Revised version received May 25, 1994 相似文献
8.
Jeannette Van Iseghem 《Numerische Mathematik》1994,68(4):549-562
Summary. A transformation of vectorial sequences is given,
analogous to the Shank's transform in the scalar case. This is possible because
of the link with the Vector Pad\'e approximants defined for a power series, with
vectorial coefficients. Algorithms, different from recursive computation of
determinants, can be defined. Some numerical examples are given.
Received December 17, 1993 / Revised version
received June 25, 1993 相似文献
9.
Stephen J. Wright 《Numerische Mathematik》1994,67(4):521-535
Summary. A parallelizable and vectorizable algorithm for
solving linear algebraic systems arising from two-point
boundary value ODEs is described. The
method is equivalent to Gaussian elimination, with
row partial pivoting, applied to a certain column-reordered
version of the usual almost-block-diagonal
coefficient matrix. We present analytical and
numerical evidence to show that the algorithm is
stable in most circumstances. Results from
implementation on a shared-memory multiprocessor
and a vector processor are given. The approach can
be extended to handle problems with multipoint and
integral conditions or with algebraic parameters.
Received April 26, 1991 / Revised version received September 3,
1993 相似文献
10.
Summary. A finite element formulation is developed for the two dimensional nonlinear time dependent compressible Navier–Stokes equations
on a bounded domain. The existence and uniqueness of the solution to the numerical formulation is proved. An error estimate
for the numerical solution is obtained.
Received September 9, 1997 / Revised version received August 12, 1999 / Published online July 12, 2000 相似文献
11.
Summary. The potential of sparse grid discretizations for solving boundary integral equations is studied for the screen problem on
a square in . Theoretical and numerical results on approximation rates, preconditioning, adaptivity and compression for piecewise constant
and linear sparse grid spaces are obtained.
Received March 17, 1998 / Revised version received September 10, 1998 相似文献
12.
Summary. The boundary element method (BEM) is of advantage in many applications including far-field computations in magnetostatics
and solid mechanics as well as accurate computations of singularities. Since the numerical approximation is essentially reduced
to the boundary of the domain under consideration, the mesh generation and handling is simpler than, for example, in a finite
element discretization of the domain. In this paper, we discuss fast solution techniques for the linear systems of equations
obtained by the BEM (BE-equations) utilizing the non-overlapping domain decomposition (DD). We study parallel algorithms for
solving large scale Galerkin BE–equations approximating linear potential problems in plane, bounded domains with piecewise
homogeneous material properties. We give an elementary spectral equivalence analysis of the BEM Schur complement that provides
the tool for constructing and analysing appropriate preconditioners. Finally, we present numerical results obtained on a massively
parallel machine using up to 128 processors, and we sketch further applications to elasticity problems and to the coupling
of the finite element method (FEM) with the boundary element method. As shown theoretically and confirmed by the numerical
experiments, the methods are of algebraic complexity and of high parallel efficiency, where denotes the usual discretization parameter.
Received August 28, 1996 / Revised version received March 10, 1997 相似文献
13.
Summary. Some micromagnetic phenomena in rigid (ferro-)magnetic materials can be modelled by a non-convex minimisation problem. Typically,
minimising sequences develop finer and finer oscillations and their weak limits do not attain the infimal energy. Solutions
exist in a generalised sense and the observed microstructure can be described in terms of Young measures. A relaxation by
convexifying the energy density resolves the essential macroscopic information. The numerical analysis of the relaxed problem
faces convex but degenerated energy functionals in a setting similar to mixed finite element formulations. The lowest order
conforming finite element schemes appear instable and nonconforming finite element methods are proposed. An a priori and a
posteriori error analysis is presented for a penalised version of the side-restriction that the modulus of the magnetic field
is bounded pointwise. Residual-based adaptive algorithms are proposed and experimentally shown to be efficient.
Received June 24, 1999 / Revised version received August 24, 2000 / Published online May 4, 2001 相似文献
14.
Summary.
Methods for the numerical inversion of a Laplace transform
which
use a special bilinear transformation of are particularly
effective in
many cases and are widely used.
The main purpose of this paper is to analyze the convergence
and conditioning
properties of a special class of such methods, characterized
by the use of
Lagrange interpolation. The results derived apply both to
complex and real
inversion, and show that some known inversion methods are in
fact in this
class.
Received
June 21, 1993 / Revised version received March 10, 1994 相似文献
15.
Christian Wagner 《Numerische Mathematik》1997,78(1):143-163
Summary. In this paper, tangential frequency filtering decompositions (TFFD) for unsymmetric matrices are introduced. Different algorithms
for the construction of unsymmetric tangential frequency filtering decompositions are presented. These algorithms yield for
a specified class of matrices equivalent decompositions. The convergence rates of an iterative scheme, which uses a sequence
of TFFDs as preconditioners, are independent of the number of unknowns for this class of matrices. Several numerical experiments
verify the efficiency of these methods for the solution of linear systems of equations which arise from the discretisation
of convection-diffusion differential equations.
Received April 1, 1996 / Revised version received July 4, 1996 相似文献
16.
Miljenko Marušić 《Numerische Mathematik》2001,88(1):135-158
Summary. The collocation tension spline is considered as a numerical solution of a singularly perturbed two-point boundary value problem:
. The collocation points are chosen as a generalization of the classical Gaussian points. Unlike the traditional approach,
we employ the B-spline representation in the analysis. This leads to global quadratic convergence of the method for small
perturbation parameters, and, for large values, the order of convergence is four.
Received October 4, 1996 / Revised version received September 23, 1999 / Published online October 16, 2000 相似文献
17.
Summary. In this paper, the multilevel ILU (MLILU) decomposition is introduced. During an incomplete Gaussian elimination process
new matrix entries are generated such that a special ordering strategy yields distinct levels. On these levels, some smoothing
steps are computed. The MLILU decomposition exists and the corresponding iterative scheme converges for all symmetric and
positive definite matrices. Convergence rates independent of the number of unknowns are shown numerically for several examples.
Many numerical experiments including unsymmetric and anisotropic problems, problems with jumping coefficients as well as realistic
problems are presented. They indicate a very robust convergence behavior of the MLILU method.
Received June 13, 1997 / Revised version received March 17, 1998 相似文献
18.
Jürgen Müller 《Numerical Algorithms》2000,24(3):299-308
Based on a continuity property of the Hadamard product of power series we derive results concerning the rate of convergence
of the partial sums of certain polynomial series expansions for Bessel functions. Since these partial sums are easily computable
by recursion and since cancellation problems are considerably reduced compared to the corresponding Taylor sections, the expansions
may be attractive for numerical purposes. A similar method yields results on series expansions for confluent hypergeometric
functions.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
19.
Christian Wagner 《Numerische Mathematik》1997,78(1):119-142
Summary. The tangential frequency filtering decomposition (TFFD) is introduced. The convergence theory of an iterative scheme based
on the TFFD for symmetric matrices is the focus of this paper. The existence of the TFFD and the convergence of the induced
iterative algorithm is shown for symmetric and positive definite matrices. Convergence rates independent of the number of
unknowns are proven for a smaller class of matrices. Using this framework, the convergence independent of the number of unknowns
is shown for Wittum's frequency filtering decomposition. Some characteristic properties of the TFFD are illustrated and results
of several numerical experiments are presented.
Received April 1, 1996 / Revised version July 4, 1996 相似文献
20.
Jae Ryong Kweon 《Numerische Mathematik》2000,86(2):305-318
Summary. We formulate the compressible Stokes system given in (1.1) into a (new) weak formulation (2.1). A finite element method for
this is presented. Existence and uniqueness of the finite element method is shown. An optimal error estimate for the numerical
approximation is obtained. Numerical examples are given, showing its efficiency and rates of convergence of the approximate
solutions that results from the discrete problem (3.1).
Received October 20, 1996 / Revised version received January 21, 1999 / Published online: April 20, 2000 相似文献