Fourier methods for smooth distribution function estimation

The limit behavior of the optimal bandwidth sequence for the kernel distribution function estimator is analyzed, in its greatest generality, by using Fourier transform methods. We show a class of distributions for which the kernel estimator achieves a first-order improvement in efficiency over the empirical estimator.     

Calculation of the orientation distribution function from a set of individual orientations on <Emphasis Type="Italic">SO</Emphasis>(3)

Kernel and projection methods for recovering the density function on the rotation group SO(3) are considered. Numerical examples are presented in which the density function is estimated depending on the sample size, a smoothing parameter (in the case of kernel methods), the approximation kernel, and the error in the input data. A set of orientations is specified by normally distributed rotations on SO(3) derived by the Monte Carlo method.     

E-Bayesian estimation for the Lomax distribution based on type-II censored data

This paper is concerned with using the E-Bayesian method for computing estimates of the unknown parameter and some survival time parameters e.g. reliability and hazard functions of Lomax distribution based on type-II censored data. These estimates are derived based on a conjugate prior for the parameter under the balanced squared error loss function. A comparison between the new method and the corresponding Bayes and maximum likelihood techniques is conducted using the Monte Carlo simulation.     

Error Estimation and Optimization of the Functional Algorithms of a Random Walk on a Grid Which Are Applied to Solving the Dirichlet Problem for the Helmholtz Equation

We consider the algorithms of a random walk on a grid which are applied to global solution of the Dirichlet problem for the Helmholtz equation (the direct and conjugate methods). In the metric space C we construct some upper error bounds and obtain optimal values (in the sense of the error bound) of the parameters of the algorithms (the number of nodes and the sample size).     

Error estimates for kernel and projection methods of recovering the orientation distribution function on <Emphasis Type="Italic">SO</Emphasis>(3)

The orientation density function is recovered from a sample of orientations on the rotation group SO(3) of the three-dimensional Euclidean space. Sufficient conditions for the consistency of kernel and projection estimates in L ₂, L ₁, and C are considered. Numerical results concerning the error estimation of projection methods over the basis of generalized spherical functions are given for normal distributions on SO(3).     

Computational scheme for invariantly unbiased estimation of linear operators in a given class

The values of linear operators of a given class are estimated in the case of measurements including piecewise continuous noise of deterministic structure with unknown parameters. A computational scheme producing unbiased linear estimates that are invariant under the noise is developed. An illustrative example is presented.     

Error analysis for the computation of zeros of regular Coulomb wave function and its first derivative

In 1975 one of the coauthors, Ikebe, showed that the problem of computing the zeros of the regular Coulomb wave functions and their derivatives may be reformulated as the eigenvalue problem for infinite matrices. Approximation by truncation is justified but no error estimates are given there.

The class of eigenvalue problems studied there turns out to be subsumed in a more general problem studied by Ikebe et al. in 1993, where an extremely accurate asymptotic error estimate is shown.

In this paper, we apply this error formula to the former case to obtain error formulas in a closed, explicit form.

     

Weak Approximation of Stochastic Differential Equations and Application to Derivative Pricing

A new, simple algorithm of order 2 is presented to approximate weakly stochastic differential equations. It is then applied to the problem of pricing Asian options under the Heston stochastic volatility model.

2000 Mathematics Subject Classification, 65C30, 65C05.     

非定常对流扩散问题差分-流线扩散法的线性三角元解的最优误差估计

讨论了差分-流线扩散法(FDSD)求解线性对流占优扩散问题解的精度,利用插值后处理技术,使该格式解的空间精间达到最优.     

Error propagation of general linear methods for ordinary differential equations

We discuss error propagation for general linear methods for ordinary differential equations up to terms of order p+2, where p is the order of the method. These results are then applied to the estimation of local discretization errors for methods of order p and for the adjacent order p+1. The results of numerical experiments confirm the reliability of these estimates. This research has applications in the design of robust stepsize and order changing strategies for algorithms based on general linear methods.     

A postprocessor for a posteriori error estimation of computed flow parameters

The possibility is explored of creating a postprocessor for a posteriori error estimation of computed target functionals based on the residual generated by a high-accuracy stencil and adjoint parameters as applied to a numerical solution. The applicability of this approach to the supersonic Euler equations is confirmed by computing the density at a control point.     

Error analysis of a fully discrete finite element variational multiscale method for time‐dependent incompressible Navier–Stokes equations

A finite element variational multiscale method based on two local Gauss integrations is applied to solve numerically the time‐dependent incompressible Navier–Stokes equations. A significant feature of the method is that the definition of the stabilization term is derived via two local Guass integrations at element level, making it more efficient than the usual projection‐based variational multiscale methods. It is computationally cheap and gives an accurate approximation to the quantities sought. Based on backward Euler and Crank–Nicolson schemes for temporal discretization, we derive error bounds of the fully discrete solution which are first and second order in time, respectively. Numerical tests are also given to verify the theoretical predictions and demonstrate the effectiveness of the proposed method. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

Error estimates of fully discrete finite element solutions for the 2D Cahn–Hilliard equation with infinite time horizon

In this article, we deal with a rigorous error analysis for the finite element solutions of the two‐dimensional Cahn–Hilliard equation with infinite time. The error estimates with respect to are proven for the fully discrete conforming piecewise linear element solution under Assumption (A1) on the initial value and Assumption (A2) on the discrete spectrum estimate in the finite element space. The analysis is based on sharp a‐priori estimates for the solutions, particularly reflecting their behavior as . Numerical experiments are carried out to support the theoretical analysis and demonstrate the efficiency of the fully discrete mixed finite element methods. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 742–762, 2017     

Complexity analysis of an interior point algorithm for the semidefinite optimization based on a kernel function with a double barrier term

In this paper, we establish the polynomial complexity of a primal-dual path-following interior point algorithm for solving semidefinite optimization(SDO) problems. The proposed algorithm is based on a new kernel function which differs from the existing kernel functions in which it has a double barrier term. With this function we define a new search direction and also a new proximity function for analyzing its complexity. We show that if q1 q2 1, the algorithm has O((q1 + 1) nq1+1/2(q1-q2)logn/ε)and O((q1 + 1)3q1-2q2+1/2(q1-q2)n~1/2 logn/ε) complexity results for large- and small-update methods, respectively.     

Two-scale analysis method for predicting heat transfer performance of composite materials with random grain distribution

A two-scale analysis (TSA) method for predicting the heat transfer performance of composite materials with the random distribution of same-scale grains is presented. First the representation of the materials with the random distribution is briefly described. Then the two-scale analysis formulation of heat transfer behavior of the materials with random grain distribution of small periodicity is formally derived by means of     

Combination of standard Galerkin and subspace methods for the time‐dependent Navier‐Stokes equations with nonsmooth initial data

We consider a combination of the standard Galerkin method and the subspace decomposition methods for the numerical solution of the two‐dimensional time‐dependent incompressible Navier‐Stokes equations with nonsmooth initial data. Because of the poor smoothness of the solution near t = 0, we use the standard Galerkin method for time interval [0, 1] and the subspace decomposition method time interval [1, ∞). The subspace decomposition method is based on the solution into the sum of a low frequency component integrated using a small time step Δt and a high frequency integrated using a larger time step pΔt with p > 1. From the H¹‐stability and L²‐error analysis, we show that the subspace decomposition method can yield a significant gain in computing time. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2009     

Error bounds for Gauss-Turán quadrature formulae of analytic functions

We study the kernels of the remainder term of Gauss-Turán quadrature formulas

for classes of analytic functions on elliptical contours with foci at , when the weight is one of the special Jacobi weights ; ; , ; , . We investigate the location on the contour where the modulus of the kernel attains its maximum value. Some numerical examples are included.

     

Error estimates of the finite element method for the exterior Helmholtz problem with a modified DtN boundary condition

A priori error estimates in the H¹- and L²-norms are established for the finite element method applied to the exterior Helmholtz problem, with modified Dirichlet-to-Neumann (MDtN) boundary condition. The error estimates include the effect of truncation of the MDtN boundary condition as well as that of discretization of the finite element method. The error estimate in the L²-norm is sharper than that obtained by the author [D. Koyama, Error estimates of the DtN finite element method for the exterior Helmholtz problem, J. Comput. Appl. Math. 200 (1) (2007) 21-31] for the truncated DtN boundary condition.     

Error estimates for the finite element solution of elliptic problems with nonlinear newton boundary conditions

The paper is concerned with the study of an elliptic boundary value problem with a nonlinear Newton boundary condition. The existence and uniqueness of the solution of the continuous pioblem is a consequence of the monotone operator theory. The main attention is paid to the investigation of the finite element approximation using numeriral integration for the evaluation of boundary integrals. The error estimates for the solution of the discrete finite element problem are derived