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1.
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
2.
Antonia Vecchio 《Numerische Mathematik》2001,89(4):783-794
Summary. Conditions are proven which assure the summability of the first difference of the fundamental matrix of nonconvolution Volterra
discrete equations. These conditions are applied to the stability analysis of some linear methods for solving Volterra integral
equations of nonconvolution type.
Received July 25, 1999 / Revised version received February 14, 2000 / Published online April 5, 2001 相似文献
3.
Andreas Rieder 《Numerische Mathematik》1997,75(4):501-522
Summary. An additive Schwarz iteration is described for the fast resolution of linear ill-posed problems which are stabilized by Tikhonov
regularization. The algorithm and its analysis are presented in a general framework which applies to integral equations of
the first kind discretized either by spline functions or Daubechies wavelets. Numerical experiments are reported on to illustrate
the theoretical results and to compare both discretization schemes.
Received March 6, 1995 / Revised version received December 27, 1995 相似文献
4.
Robert Plato 《Numerische Mathematik》1996,75(1):99-120
Summary. For the numerical solution of (non-necessarily well-posed) linear equations in Banach spaces we consider a class of iterative
methods which contains well-known methods like the Richardson iteration, if the associated resolvent operator fulfils a condition
with respect to a sector. It is the purpose of this paper to show that for given noisy right-hand side the discrepancy principle
(being a stopping rule for the iteration methods belonging to the mentioned class) defines a regularization method, and convergence
rates are proved under additional smoothness conditions on the initial error. This extends similar results obtained for positive
semidefinite problems in Hilbert spaces. Then we consider a class of parametric methods which under the same resolvent condition
contains the method of the abstract Cauchy problem, and (under a weaker resolvent condition) the iterated method of Lavrentiev.
A modified discrepancy principle is formulated for them, and finally numerical illustrations are presented.
Received August 29, 1994 / Revised version received September 19, 1995 相似文献
5.
Summary. Both mixed finite element methods and boundary integral methods are important tools in computational mechanics according to
a good stress approximation. Recently, even low order mixed methods of Raviart–Thomas-type became available for problems in
elasticity. Since either methods are robust for critical Poisson ratios, it appears natural to couple the two methods as proposed
in this paper. The symmetric coupling changes the elliptic part of the bilinear form only. Hence the convergence analysis
of mixed finite element methods is applicable to the coupled problem as well. Specifically, we couple boundary elements with
a family of mixed elements analyzed by Stenberg. The locking-free implementation is performed via Lagrange multipliers, numerical
examples are included.
Received February 21, 1995 / Revised version received December 21, 1995 相似文献
6.
Summary. We prove convergence results and error estimates for interpolatory product quadrature formulas for Cauchy principal value
integrals on the real line with Freud–type weight functions. The formulas are based on polynomial interpolation at the zeros
of orthogonal polynomials associated with the weight function under consideration. As a by–product, we obtain new bounds for
the derivative of the functions of the second kind for these weight functions.
Received July 15, 1997 / Revised version received August 25, 1998 相似文献
7.
Summary.
Rank-revealing decompositions are favorable alternatives to the
singular value decomposition (SVD) because they are faster to compute
and easier to update.
Although they do not yield all the information that the SVD does,
they yield enough information to solve various problems because they
provide accurate bases for the relevant subspaces.
In this paper we consider rank-revealing decompositions in
computing estimates of
the truncated SVD (TSVD) solution to an overdetermined system of
linear equations
, where
is numerically rank deficient.
We derive analytical bounds which show how the accuracy of the solution
is intimately connected to the quality of the subspaces.
Received
July 12, 1993 / Revised version received November 14,
1994 相似文献
8.
Summary. We combine a primal mixed finite element approach with a Dirichlet-to-Neumann mapping (arising from the boundary integral
equation method) to study the weak solvability and Galerkin approximations of a class of linear exterior transmission problems
in potential theory. Our results are mainly based on the Babuska-Brezzi theory for variational problems with constraints.
We establish the uniqueness of solution for the continuous and discrete formulations, and show that finite element subspac
es of Lagrange type satisfy the discrete compatibility conditions. In addition, we provide the error analysis, including polygonal
approximations of the domain, and prove strong convergence of the Galerkin solutions. Moreover, under additional regularity
assumptions on the solution of the continuous formulation, we obtain the asymptotic rate of convergence O(h).
Received August 25, 1998 / Revised version received March 8, 2000 / Published online October 16, 2000 相似文献
9.
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
10.
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
11.
Carsten Carstensen 《Numerische Mathematik》1999,82(4):577-597
Summary. The finite element method is a reasonable and frequently utilised tool for the spatial discretization within one time-step
in an elastoplastic evolution problem. In this paper, we analyse the finite element discretization and prove a priori and
a posteriori error estimates for variational inequalities corresponding to the primal formulation of (Hencky) plasticity.
The finite element method of lowest order consists in minimising a convex function on a subspace of continuous piecewise linear
resp. piecewise constant trial functions. An a priori error estimate is established for the fully-discrete method which shows
linear convergence as the mesh-size tends to zero, provided the exact displacement field u is smooth. Near the boundary of the plastic domain, which is unknown a priori, it is most likely that u is non-smooth. In this situation, automatic mesh-refinement strategies are believed to improve the quality of the finite
element approximation. We suggest such an adaptive algorithm on the basis of a computable a posteriori error estimate. This
estimate is reliable and efficient in the sense that the quotient of the error by the estimate and its inverse are bounded
from above. The constants depend on the hardening involved and become larger for decreasing hardening.
Received May 7, 1997 / Revised version received August 31, 1998 相似文献
12.
Summary. A numerical method for solving the thermal subproblem appearing in the modelization of polythermal ice sheets is described.
This thermal problem mainly involves three nonlinearities: a reaction term due to the viscous dissipation, a Signorini boundary
condition associated to the geothermic flux and an enthalpy term issued from the two phase Stefan formulation of the polythermal
regime. The stationary temperature is obtained as the limit of an evolutive problem which is discretized in time with an upwind
characteristics scheme and in space with finite elements. The nonlinearities are solved either by Newton-Raphson method or
by duality techniques applied to maximal monotone operators. The application of the algorithms provides the dimensionless
temperature distribution approximation and allows to identify the cold and temperate ice regions.
Received February 1, 1998 / Published online July 28, 1999 相似文献
13.
Summary. Conformal maps from the exterior of the closed unit disk onto the exterior of ‘bratwurst’ shape sets in the complex plane
are constructed. Using these maps, coefficients for the computation of the corresponding Faber polynomials are derived. A
‘bratwurst’ shape set is the result of deforming an ellipse with foci on the real axis, by conformally mapping the real axis
onto the unit circle. Such sets are well suited to serve as inclusion sets for sets associated with a matrix, for example
the spectrum, field of values or a pseudospectrum. Hence, the sets can be applied in the construction and analysis of a broad
range of iterative methods for the solution of linear systems. The main advantage of the approach is that the conformal maps
are derived from elementary transformations, allowing an easy computation of the associated transfinite diameter, asymptotic
convergence factor and Faber polynomials. Numerical examples are given.
Received October 7, 1998 / Revised version received March 15, 1999 / Published online April 20, 2000 –? Springer-Verlag 2000 相似文献
14.
A self-sorting in-place fast Fourier
transform algorithm suitable for vector and parallel
processing
Markus Hegland 《Numerische Mathematik》1994,68(4):507-547
Summary.
We propose a new algorithm for fast Fourier transforms. This
algorithm features uniformly long vector lengths and stride one
data access. Thus it is well adapted to modern vector
computers like the Fujitsu VP2200 having several floating point
pipelines per CPU and very fast stride one data access. It also
has favorable properties for distributed memory computers as
all communication is gathered together in one step. The
algorithm has been implemented on the Fujitsu VP2200 using the
basic subroutines for fast Fourier transforms discussed
elsewhere.
We develop the theory of index digit permutations to some
extent. With this theory we can derive the splitting formulas
for almost all mixed-radix FFT algorithms known so far. This
framework enables us to prove these algorithms but also to
derive our new algorithm. The development and systematic use of
this framework is new and allows us to simplify the
proofs which are now reduced to the application of matrix
recursions.
Received October 29, 1992 / Revised version received
October 21, 1993 相似文献
15.
Summary. The qualocation methods developed in this paper, with spline trial and test spaces, are suitable for classes of boundary
integral equations with convolutional principal part, on smooth closed curves in the plane. Some of the methods are suitable
for all strongly elliptic equations; that is, for equations in which the even symbol part of the operator dominates. Other
methods are suitable when the odd part dominates.
Received December 27, 1996 / Revised version received April 14, 1997 相似文献
16.
Summary. Here the stability and convergence results of oqualocation methods providing additional orders of convergence are extended
from the special class of pseudodifferential equations with constant coefficient symbols to general classical pseudodifferential
equations of strongly and of oddly elliptic type. The analysis exploits localization in the form of frozen coefficients, pseudohomogeneous
asymptotic symbol representation of classical pseudodifferential operators, a decisive commutator property of the qualocation
projection and requires qualocation rules which provide sufficiently many additional degrees of precision for the numerical
integration of smooth remainders. Numerical examples show the predicted high orders of convergence.
Received January 29, 1998 / Published online: June 29, 1999 相似文献
17.
Summary. The objective of this paper is to introduce a fast algorithm for computing the integral wavelet transform (IWT) on a dense
set of points in the time-scale domain. By applying the duality principle and using a compactly supported spline-wavelet as
the analyzing wavelet, this fast integral wavelet transform (FIWT) is realized by applying only FIR (moving average) operations,
and can be implemented in parallel. Since this computational procedure is based on a local optimal-order spline interpolation
scheme and the FIR filters are exact, the IWT values so obtained are guaranteed to have zero moments up to the order of the
cardinal spline functions. The semi-orthogonal (s.o.) spline-wavelets used here cannot be replaced by any other biorthogonal
wavelet (spline or otherwise) which is not s.o., since the duality principle must be applied to some subspace of the multiresolution
analysis under consideration. In contrast with the existing procedures based on direct numerical integration or an FFT-based
multi-voice per octave scheme, the computational complexity of our FIWT algorithm does not increase with the increasing number
of values of the scale parameter.
Received March 3, 1994 相似文献
18.
Summary. We apply multiscale methods to the coupling of finite and boundary element methods to solve an exterior Dirichlet boundary
value problem for the two dimensional Poisson equation. Adopting biorthogonal wavelet matrix compression to the boundary terms
with N degrees of freedom, we show that the resulting compression strategy fits the optimal convergence rate of the coupling Galerkin
methods, while the number of nonzero entries in the corresponding stiffness matrices is considerably smaller than .
Received December 3, 1999 / Revised version received September 22, 2000 / Published online December 18, 2001 相似文献
19.
Kai Diethelm 《Numerische Mathematik》1996,73(1):53-63
Summary.
We show that, if
(),
the error term of
every modified positive interpolatory quadrature rule for
Cauchy principal value integrals of the type
,
, fulfills
uniformly for all
, and hence it is
of optimal
order of magnitude in the classes
().
Here, is a weight function with the property
.
We give explicit upper bounds for the Peano-type error
constants of such rules.
This improves and completes earlier results by
Criscuolo and Mastroianni
(Calcolo 22 (1985), 391–441 and Numer. Math.
54 (1989), 445–461)
and Ioakimidis (Math. Comp. 44 (1985), 191–198).
For the special case of the Gaussian rule, we
show that the restriction
can be dropped.
The results are based on a new representation of the
Peano kernels of these formulae via the Peano kernels of the underlying
classical quadrature formulae. This representation may also be
useful in connection with some different problems.
Received November 21, 1994 相似文献
20.
Summary. The aim of this paper is to prove some Babuška–Brezzi type conditions which are involved in the mortar spectral element discretization
of the Stokes problem, for several cases of nonconforming domain decompositions.
ID=" <E5>Dedicated to Olof B. Widlund on the occasion of his 60th birthday</E5> 相似文献