Multilevel Iteration Research Articles

Unpacking the relation between learning orientation and product innovation: Does strategic flexibility matter?

Abstract Learning orientation emphasizes the importance of learning from any experience. It is grounded on commitment to learn, shared vision, open‐mindedness, and knowledge sharing. Organizational knowledge management literature based on social complexity theory posits that learning orientation makes companies generate new knowledge through spontaneous multi-level iterations and self-organization. Challenges related to the current business environment requires companies to constantly adjust to remain competitive. Still, the mechanisms making learning-oriented companies more capable to develop innovative product have been scantly explored. Pertinent literature actually conjectures this relationship as spontaneous, directed, and unmediated. Moreover, Small and Medium Enterprises (SMEs)rarely represent the context of analysis of research on this topic. Frequently lacking resources to systematically pursue product innovation, SMEs rely on solutions deriving from the combination of internal knowledge and external sources; thus, these companies depend on learning orientation principles to remain innovative. In this vein, the research aims to understand how learning orientation allows product innovation in SMEs through the achievement of strategic flexibility. Structural equation modelling was used to analyse data from 300 British SMEs. The results demonstrate the mediating role of strategic flexibility in the relationships between learning orientation and product innovation. The importance of innovation culture also emerged.

Fast multi-level iteration schemes with compression technique for eigen-problems of compact integral operators

In this paper, we present multi-level iteration schemes to solve the eigen-problems of compact integral operators based on the multiscale Galerkin methods. By using the compression technique, the wavelet coefficient matrix is truncated into sparse. This technique results in a fast algorithm. To further minimize computational complexity, we establish Jacobi, Gauss-Seidel and L-H iteration schemes for solving the final algebraic eigenvalue problems obtained from discretizing the integral equation using fast multiscale Galerkin methods. We show that the proposed schemes require only linear computational complexity and obtain the desired convergence order for the approximate eigenvalues and eigenvectors. Numerical experiments are conducted and analyzed, with comparisons to the standard routine and the power iteration algorithm included. Ultimately, our multi-level iteration schemes yield faster solutions with fewer iterations, which is independent of the dimension of approximate space.

A New Method of Frequency Fluctuation Estimation and IPS Processing Results Based on the Downlink Signal of Tianwen-1

The radio-occultation observations taken by Tianwen-1 are aiming to study the properties of solar wind. A new method of frequency fluctuation (FF) estimation is presented for processing the down-link signals of Tianwen-1 during the occultation period to study the properties of the coronal plasma at the heliocentric distances of 4.48–19 R ⊙. Because of low S/N as well as the phase fluctuation phenomena caused by solar activity, a Kalman based on polynomial prediction methods is proposed to avoid the phase locked loop loss lock. A new detrend method based on multi-level iteration correction is proposed to estimate Doppler shift to get more accurate power density spectra of FF in the low frequency region. The data analyze procedure is used to get the properties of the solar corona during the occultation. The method was finally verified at the point when the solar offset is 5.7 R ⊙, frequency tracking was successfully performed on data with a carrier-to-noise ratio of about 28 dBHz. The density spectra obtained by the improved method are basically the same when the frequency is greater than 2 mHz, the uncertainty in the result of the rms of the FF obtained by removing the trend term with different order polynomials is less than 3.3%. The data without eliminating interference show a large error for different detrending orders, which justifies the need for an improved approach. Finally, the frequency fluctuation results combined with the information on intensity fluctuation obtained by the new method are compared with the results of the integrated Space Weather Analysis system and theoretical formula, which verifies that the processing results in this paper have a certain degree of credibility.

Fast multilevel iteration methods for solving nonlinear ill-posed problems

Abstract We propose a multilevel iteration method for the numerical solution of nonlinear ill-posed problems in the Hilbert space by using the Tikhonov regularization method. This leads to fast solutions of the discrete regularization methods for the nonlinear ill-posed equations. An adaptive choice of an a posteriori rule is suggested to choose the stopping index of iteration, and the rates of convergence are also derived. Numerical results are presented to demonstrate the efficiency and accuracy of the proposed method.

Adaptive multilevel iteration methods for solving ill-posed integral equations via a coupled system

An adaptive multilevel iteration method via a coupled system is proposed, which leads to fast and effective algorithm for solving ill-posed integral equations. In this algorithm, the discrete layer and the iteration can be selected adaptively. By imposing projection conditions, convergence rates of an a priori parameter choice rule and two a posteriori parameter choice rule for this algorithm are established under certain source conditions. Numerical results are presented to illustrate the performance of adaptive multilevel iteration methods with the balance principle and the discrepancy principle, respectively.

The Dynamic Interplay Between Antecedents of Technical Innovation: Evidence From China

Antecedents of technical innovation trigger firms to perceive changes in demand in emerging markets, thereby facilitating firms to update their primary technologies accordingly. These factors predicting firms’ activities vary across hierarchies, stages, and categories, but they jointly affect firms’ exploration and exploitation activities in technical fields. Previous research reveals how different antecedents lead to heterogeneity in firms’ innovative actions. However, there is still a lack of analyses on the associations between such antecedents. To fill this gap, our empirical research proposed endogenous links among predictors from three perspectives. First, firms’ updating processes in technical domains exhibit a specific type of iterative procedure across multiple market levels, including those at the firm, industry, and national levels. The antecedents of such innovation mutually affect each other within this multi-level iteration. Furthermore, some antecedents that arise at certain stages possibly lead to the appearance of others in later phases, that is, their relationships are reciprocal. Third, the predictive factors of firms’ technical innovation can be categorized into groups based on their features. Cause-effect relationships exist between the identities of these groups. We focused on Chinese technology markets, particularly the technical catch-up phenomenon, and employed a pertinence survey to test our hypotheses. Our findings indicate the associations between technical innovation antecedents and the effects of endogeneity problems on these relationships, thus providing practical implications and directions for future research in relevant areas.

A fast multilevel iteration method for solving linear ill-posed integral equations

Abstract We propose a new concept of noise level: R ⁢ ( K * ) \mathcal{R}(K^{*}) -noise level for ill-posed linear integral equations in Tikhonov regularization, which extends the range of regularization parameter. This noise level allows us to choose a more suitable regularization parameter. Moreover, we also analyze error estimates of the approximate solution with respect to this noise level. For ill-posed integral equations, finding fast and effective numerical methods is a challenging problem. For this, we formulate a matrix truncated strategy based on multiscale Galerkin method to generate the linear system of Tikhonov regularization for ill-posed linear integral equations, which greatly reduce the computational complexity. To further reduce the computational cost, a fast multilevel iteration method for solving the linear system is established. At the same time, we also prove convergence rates of the approximate solution obtained by this fast method with respect to the R ⁢ ( K * ) \mathcal{R}(K^{*}) -noise level under the balance principle. By numerical results, we show that R ⁢ ( K * ) \mathcal{R}(K^{*}) -noise level is very useful and the proposed method is a fast and effective method, respectively.

Fast moving horizon estimation using multi-level iterations for microgrid control

Abstract Accurate state-estimation is a vital prerequisite for fast feedback control methods such as Nonlinear Model Predictive Control (NMPC). For efficient process control, it is of great importance that the estimation process is carried out as fast as possible to provide the feedback mechanism with fresh information and enable fast reactions in case of any disturbances. We discuss how Multi-Level Iterations (MLI), known from NMPC, can be applied to the Moving Horizon Estimation (MHE) method for estimating the states and parameters of a system described by a Differential Algebraic Equation model. A challenging field of application for the proposed MLI-MHE method are electric microgrids. These push current control approaches to their limits due to the rising penetration of volatile renewable energy sources and the fast electrical system dynamics. We investigate the closed-loop control performance of the proposed MLI-MHE algorithm in combination with an NMPC controller for a realistic sized microgrid as a numerical example.

Fault diagnosis of shipboard medium-voltage DC power system based on machine learning

This study proposed a fault diagnosis method of a shipboard medium-voltage DC (MVDC) power system based on Noise-Assisted Multivariate Empirical Mode Decomposition (NA-MEMD) and Multilevel Iterative – LightGBM (MI-LightGBM), which overcomes the limitations of the existing fault diagnosis methods in this regard, such as relies heavily on the relay or slow training process. MI-LightGBM is proposed to solve the problem of unbalanced training samples caused by the difficulty in obtaining fault samples in practical engineering. First, NA-MEMD was adopted to pre-process the voltage signals, which were decomposed into a set of components called Intrinsic Mode Functions (IMFs) according to the local characteristic time scales of the original signals. The energy moment of each order IMF was calculated as fault feature vector to train the MI-LightGBM model, which led to the development of a high-precision fault classifier. A model of a shipboard MVDC power system was established using the AppSIM Real-Time Simulator. Simulations were performed on earth fault and short-circuit fault at the generator output and DC cable. Compared with the existing fault diagnosis methods, the proposed method is simple to use and save more than half of the training time while maintaining high diagnostic performance, which is more suitable for engineering applications.

A Multilevel Iteration Method for Solving a Coupled Integral Equation Model in Image Restoration

The problem of out-of-focus image restoration can be modeled as an ill-posed integral equation, which can be regularized as a second kind of equation using the Tikhonov method. The multiscale collocation method with the compression strategy has already been developed to discretize this well-posed equation. However, the integral computation and solution of the large multiscale collocation integral equation are two time-consuming processes. To overcome these difficulties, we propose a fully discrete multiscale collocation method using an integral approximation strategy to compute the integral, which efficiently converts the integral operation to the matrix operation and reduces costs. In addition, we also propose a multilevel iteration method (MIM) to solve the fully discrete integral equation obtained from the integral approximation strategy. Herein, the stopping criterion and the computation complexity that correspond to the MIM are shown. Furthermore, a posteriori parameter choice strategy is developed for this method, and the final convergence order is evaluated. We present three numerical experiments to display the performance and computation efficiency of our proposed methods.

An overview of numerical methods for the first kind Fredholm integral equation

In the field of engineering technology, many problems can be transformed into the first kind Fredholm integral equation, which has a prominent feature called “ill-posedness”. This property makes it difficult to find the analytical solution of first kind Fredholm integral equation. Therefore, how to find the numerical solution of first kind Fredholm integral equation has been a common concern of domestic and overseas scholars in recent years. In this article, various numerical solution methods of first kind Fredholm integral equation are introduced in detail. First, the existence and convergence of the solution of the integral equation are given. Second, the current mainstream numerical methods, such as regularization method, wavelet analysis method and multilevel iteration method are introduced in detail. Finally, we presented a concise overview of the numerical method of first kind Fredholm integral equation.

Low-rank improvements of two-level grid preconditioned matrices

As an alternative to basic two-level and multilevel iteration preconditioners for elliptic partial differential equations, it is shown that low-rank approximations, based on approximate eigenvectors to the largest eigenvalues of the inverse two-level Schur complement matrix, can give arbitrarily accurate preconditioners that hold uniformly with respect to mesh sizes. The methods are particularly efficient for problems with multiple right hand sides.

Multigrid methods for convection–diffusion problems discretized by a monotone scheme

We study multigrid (MG) methods for the solution of systems of linear algebraic equations obtained from a stable discretization of convection–diffusion problems by an exponential fitting scheme. The latter ensures the stability of the simplest possible coarse grid operators obtained from Galerkin projections based on graph matching. Linear and nonlinear MG preconditioners are defined in the framework of algebraic multilevel iteration. The option of using polynomial smoothers is investigated in context of nonsymmetric problems and a systematic performance comparison is presented for various algorithms on a representative set of two- and three-dimensional test problems.

Preconditioned Multigroup GMRES Algorithms for the Variational Nodal Method

Combinations of three approaches are examined as options to replace the algorithms presently employed in the variational nodal code VARIANT. They are preconditioned Generalized Minimal Residual (GMRES) algorithms, parallelism in energy, and Wielandt acceleration. Together with partitioned matrix and Gauss-Seidel (GS) preconditioners, two GMRES algorithms are formulated to replace the upscattering iteration and facilitate energy parallelism and Wielandt acceleration. The GMRES algorithms are tested on two-dimensional thermal and fast reactor diffusion problems. The two GMRES algorithms yield higher efficiencies in energy group parallelization and Wielandt acceleration than simple parallelization of the existing GS algorithm. With preconditioning the GMRES algorithms reduce the total computing time by a factor of 2 to 4 and in some cases by a factor of >10.A multilevel iteration optimization scheme is investigated that automatically adjusts the relative error tolerance of the inner iterations according to the estimated convergence rate of the corresponding outer iterations and updates the Wielandt shift magnitude as the calculations progress. Numerical results based on large two-dimensional thermal and fast reactor diffusion problems demonstrate that automated optimization of the multilevel iterative processes reduces iteration numbers by as much as an order of magnitude.

A Novel Intrusion Detection Model for Mobile Ad-Hoc Networks using CP-KNN

Mobile ad-hoc network security problems are the subject of in depth analysis. A group of mobile nodes area unit connected to a set wired backbone. In MANET, the node themselves implement the network management in a very cooperative fashion. All the nodes area unit accountable to create a constellation that is dynamically, modification it and conjointly the absence of any clear network boundaries. We tend to project a completely unique intrusion detection model for mobile ad-hoc network victimization. CP-KNN (Conformal Prediction K-Nearest Neighbor) algorithmic rule is to classify the audit knowledge for anomaly detection. The non-conformity score worth is employed to cut back the classification period of time for multi level iteration. It is effectively notice anomalies with high true positive rate, low false positive rate and high confidence that the progressive of assorted anomaly detection ways. Additionally it is interfered by “noisy” knowledge (unclean data), the projected technique is strong, effective and conjointly it retains its smart detection performance and to avoid the abnormal activity.

Semi-coarsening AMLI preconditioning of anisotropic trilinear FEM systems

Optimal order algebraic multilevel iteration (AMLI) preconditioners based on recursive application of two-level finite element (FE) methods and polynomial stabilization have been introduced and analyzed in Axelsson and Vassilevski (1989, 1990). The construction follows the natural hierarchical splitting using the fact that the finite element spaces corresponding to two successive mesh refinements are nested. Uniform estimates for the constant γ in the strengthened Cauchy–Bunyakowski–Schwarz (CBS) inequality are very important for the derivation of optimal order methods. The value of the upper bound for γ∈(0,1) is a part of the construction of the multilevel extension of the related two-level method.In this paper algebraic two-level and multilevel preconditioning algorithms for second order anisotropic elliptic boundary value problems are constructed. Here we allow big jumps in the coefficients and varying the direction of dominating anisotropy from one element to another in the coarse triangulation. The discretization is done by trilinear conforming finite elements where the semi-coarsening mesh refinement strategy is applied. A new uniform estimates for the related CBS constants are derived. The additive preconditioning strategy for the system with the pivot block in the hierarchical two-level splitting is proposed, where the related sub-problems have two dimensional structure.

Robust Multilevel Methods for General Symmetric Positive Definite Operators

A general robust multilevel method for solving symmetric positive definite systems resulting from discretizing elliptic partial differential equations is developed. The term “robust” refers to the convergence rate of the method being independent of discretization parameters, i.e., the problem size, and problem parameters. Important instances of such problem parameters are in particular (highly varying) coefficients. The method belongs to the class of (nonlinear) algebraic multilevel iterations. The crucial ingredient for obtaining robustness is the construction of a nested sequence of spaces based on local generalized eigenvalue problems. The method is analyzed in a rather general setting applying to the scalar elliptic equation, the equations of linear elasticity, and equations arising in the solution of Maxwell's equations. Numerical results for the scalar elliptic equation are presented showing its robust convergence behavior.

Robust algebraic multilevel preconditioning in [formula omitted] and [formula omitted

An algebraic multilevel iteration method for solving a system of linear algebraic equations arising in H(curl) and H(div) spaces is presented. The algorithm is developed for the discrete problem obtained by using the space of lowest-order Nedelec and Raviart–Thomas–Nedelec elements. The theoretical analysis of the method is based only on some algebraic sequences and generalized eigenvalues of local (element-wise) problems. In the hierarchical basis framework, explicit recursion formulas are derived to compute the element matrices and the constant γ (which measures the quality of the space splitting) at any given level. It is proved that the proposed method is robust with respect to the problem parameters and is of optimal order complexity. Supporting numerical results, including the case when the parameters have jumps, are also presented.

Fast multi-level iteration methods with compression technique for solving ill-posed integral equations

We develop a multilevel iteration method with compression technique for solving ill-posed integral equations. The method leads to fast solutions of discrete regularization methods for the equations. Choice for a posteriori regularization parameter is proposed. An optimal convergence order for the method with the choices of parameters is established. The theoretical analysis and numerical experiments illustrate the accuracy and efficiency of the algorithm.

Algebraic multilevel preconditioning in isogeometric analysis: Construction and numerical studies

We present algebraic multilevel iteration (AMLI) methods for isogeometric discretization of scalar second order elliptic problems. The construction of coarse grid operators and hierarchical complementary operators are given. Moreover, for a uniform mesh on a unit interval, the explicit representation of B-spline basis functions for a fixed mesh size h is given for p=2,3,4 and for C0- and Cp-1-continuity. The presented methods show h- and (almost) p-independent convergence rates. Supporting numerical results for convergence factor and iterations count for AMLI cycles (V-, linear W-, nonlinear W-) are provided. Numerical tests are performed, in two-dimensions on square domain and quarter annulus, and in three-dimensions on quarter thick ring.