Iterative Refinement Technique Research Articles

Adaptive Spline Surface Fitting With Arbitrary Topological Control Mesh.

Reconstructing a spline surface from a given arbitrary topological triangle mesh is a fundamental and challenging problem in computer-aided design and engineering. This article introduces a novel surface fitting method utilizing G-NURBS capable of handling control meshes with arbitrary topologies. This method employs adaptive control point adjustment, guided by the geometric attributes of the input model, ensuring precise representation of sharp features such as edges and corners. Two primary strategies are employed: A parameter correspondence approach designed for sharp features and a control mesh iterative refinement technique that incorporates geometrical feature information. The proposed method has been tested and evaluated on various CAD models to demonstrate its effectiveness. This method can achieve higher fitting accuracy while faithfully preserving the geometrical features with fewer control points.

Enhancing cubic polynomial solutions: A comprehensive analysis and iterative refinement strategy in response to the versatility of cubic equations of state

The study presents a comprehensive evaluation of ten distinct methods for solving cubic equations, encompassing both analytical, numerical, and linear algebra-based approaches. Among these, an analytical technique involving the transformation of cubic equations into Chebyshev polynomials emerged as the most efficient. To mitigate issues arising from numerical round-off errors, the study proposes an iterative refinement strategy. Furthermore, the research introduces a novel criterion grounded in Vieta's formulas to identify and isolate areas where round-off errors may occur. This criterion aids in the application of the proposed iterative refinement technique. The novel solution method, which involves the conversion of cubic equations into Chebyshev polynomials and subsequent error-checking and iterative refinement, exhibits significant advantages. Firstly, it proves efficient, reducing computational time by 15–20 % in comparison to the well-established Cardano analytical method. It also demonstrates robustness in effortlessly identifying regions of potential error and offers a method for iterative improvement when needed. Additionally, its reliability is underscored by its independence from the specific cubic equation of state under consideration, making it well-suited for the intensive solution of a wide range of cubic equations.

Distributed Optimization Design of Iterative Refinement Technique for Algebraic Riccati Equations

This article focuses on the problem of a distributed computation of continuous-time algebraic Riccati equations (CARE), where information of matrices is split and known by multiple agents. This article proposes a distributed optimization design of the iterative refinement technique (IRM), a well-established centralized method for CARE. By assuming that each agent only knows partial information of CARE, we reformulate IRM for CARE as three classes of distributed optimization subproblems with different formulations and constraints. Then, we propose distributed algorithms for obtained distributed optimization subproblems and prove convergence properties of proposed algorithms. Numerical results show the efficacy of the proposed distributed IRM.

Leveraging Iterative Plan Refinement for Reactive Smart Manufacturing Systems

Industry 4.0 production systems must support flexibility in various dimensions, such as for the products to be produced, for the production processes to be applied, and for the available machinery. In this article, we present a novel approach to design and control smart manufacturing systems. The approach is reactive, that is responds to unplanned situations and implements an iterative refinement technique, that is, optimizes itself during runtime to better accommodate production goals. For realizing these advances, we present a model-driven methodology and we provide a prototypical implementation of such a production system. In particular, we employ Planning Domain Definition Language (PDDL) as our artificial intelligence environment for automated planning of production processes and combine it with one of the most prominent Industry 4.0 standards for the fundamental production system model: IEC 62264. We show how to plan the assembly of small trucks from available components and how to assign specific production operations to available production resources, including robotic manipulators and transportation system shuttles. Results of the evaluation indicate that the presented approach is feasible and that it is able to significantly strengthen the flexibility of production systems during runtime. Note to Practitioners —Smart production is an umbrella for a number of shifts and initiatives that deal with digitization of manufacturing/production systems and related issues and potentials. In this work, we present an approach for utilizing automated planning for creating production plans. This is in contrast to the traditional approach, where recipes are programmed into the production system ahead-of-time. However, automated planning relies on specific languages and tools that are hard to master by nonexperts, which is a factor that strongly limited the utilization of plan-driven approaches for industrial automation in practice. Thus, we propose to generate planning tasks automatically with model-driven engineering techniques. We are utilizing the industrial standard IEC 62264 for the description of the production system, and the academic standard Planning Domain Definition Language (PDDL) for planning. PDDL is handled completely transparent to the user, that is the user is shielded from its complexity by employing the IEC 62264 model as the sole frontend.

A flexible calibration method for the intrinsic and mechanical parameters of panoramic line-scan cameras

Panoramic line-scan cameras provide high definition images with a quasi uniform distribution of the sensing elements. Unfortunately, calibration of such devices with classic techniques is not possible making their use, in computer vision field, not straightforward. We propose a flexible and convenient calibration method for the computation of intrinsic and mechanism parameters of such systems by using images of a simple calibration pattern. Unlike existing approaches, the proposed method considers a full geometrical model and does not make any unattainable assumption such as concentricity of images, a priori knowledges about camera poses or coincidence of the rotation axis with the optical center. Using few images taken with free poses, the calibration is performed in two steps. First, the intrinsic parameters are computed using sets of 2D/3D point correspondences that are generated automatically by exploiting the structure of the calibration rig. Then, thanks to the parameterization of the projection of a 3D straight line, the mechanical parameters are computed using points at infinity. For each step, closed form solutions and iterative refinement techniques are presented. The proposed approach is validated with both synthetic and real data collected by our prototype.

Target Localization in Multipath Propagation Environment Using Dictionary-Based Sparse Representation

This paper addresses the target localization problem in complex multipath propagation environment for three-dimensional (3-D) radar systems. Firstly, an approach based on the singular value decomposition (SVD) technique is developed to reduce the data dimension and formulate the joint multiple snapshot sparse representation problem in the signal subspace domain. Subsequently, a novel sparse representation based DOA estimation algorithm, combined with alternatingly iterative and dictionary refinement techniques, is proposed. The Cramer-Rao bounds (CRB) for the target DOA and attenuation coefficient estimations of multipath model are derived in closed forms. Experimental results based on both simulated data and measured data indicate that the target localization accuracy can be effectively enhanced by utilizing the proposed algorithm in complex terrain and/or limited snapshot scenarios.

Iterative Refinement of Accelerations in Real-Time Vehicle Dynamics

A number of strategies can be followed for the real-time simulation of multibody systems. The main contributing factor to computational efficiency is usually the algorithm itself (the number of equations and their structure, the number of coordinates, the time integration scheme, etc.). Additional (but equally important) aspects have to do with implementation (linear solvers, sparse matrices, parallel computing, etc.). In this paper, an iterative refinement technique is introduced into a semirecursive multibody formulation. First, the formulation is summarized and its basic features are highlighted. Then, the basic goal is to iteratively solve the fundamental system of equations to obtain the accelerations. The iterative process is applied to compute corrections of the solution in an economic way, terminating as soon as a given precision is reached. We show that, upon implementation of this method, the computation time can be reduced at a very low implementation and accuracy costs. Two vehicles are simulated to prove the numerical benefits, namely a 16-degrees-of-freedom (DOF) sedan vehicle and a 40-degrees-of-freedom semitrailer truck. In short, a simple method to iteratively solve for the accelerations of vehicle systems in an efficient way is presented.

Parallel Transient Stability-Constrained Optimal Power Flow Using GPU as Coprocessor

Graphics processing unit (GPU) has significantly increased the computing capacity of state-of-the-art high performance computing systems. This paper presents a novel GPU acceleration approach for transient stability-constrained optimal power flow (TSCOPF), which is one of the most computational challenging tasks in large-scale power system applications. Enabled by the revealed two-level decomposition parallelism in reduced-space interior point method, GPUs serve as plug-and-play coprocessors for time-consuming linear algebra operations in TSCOPF solving. Enhanced by multi-GPU processing and mixed-precision iterative refinement technique, the efficiency of solving TSCOPF is greatly improved without redesigning and reimplementing the existing algorithm framework. Numerical studies based on a series of test cases with up to 12 951 buses indicate the effectiveness of the proposed GPU-based approach for large-scale TSCOPF problems.

A note on the Davison–Man method for Sylvester matrix equations

In this paper, we introduce a modernized and improved version of the Davison–Man method for the numerical resolution of Sylvester matrix equations. In the case of moderate size problems, we give some background facts about this iterative method, addressing the problem of stagnation and we propose an iterative refinement technique to improve its accuracy. Although not designed to solve large-scale Sylvester equations, we propose an approach combining the extended block Krylov algorithm and the Davison–Man method which gives interesting results in terms of accuracy and shows to be competitive with the classical Krylov subspaces methods. Numerical examples are given to illustrate the efficiency of this approach.

Combined probabilistic algorithm for solving high dimensional problems

The present study establishes an accurate and efficient algorithm based on Monte Carlo (MC) simulation for solving high dimensional linear systems of algebraic equations (LSAEs) and two-dimensional Fredholm integral equations of the second kind (FIESK). This new combined numerical-probabilistic algorithm is based on Jacobi over-relaxation method and MC simulation in conjunction with the iterative refinement technique to find the unique solution of the large sparse LSAEs. It has an excellent accuracy, low cost and simple structure. Theoretical results are established to justify the convergence of the algorithm. To confirm the accuracy and efficiency of the present work, the proposed algorithm is used for solving and LSAEs. Furthermore, the algorithm is coupled with Galerkin's method to illustrate the power and effectiveness of the proposed algorithm for solving two-dimensional FIESK.

A survey of recent developments in parallel implementations of Gaussian elimination

SummaryGaussian elimination is a canonical linear algebra procedure for solving linear systems of equations. In the last few years, the algorithm has received a lot of attention in an attempt to improve its parallel performance. This article surveys recent developments in parallel implementations of Gaussian elimination for shared memory architecture. Five different flavors are investigated. Three of them are based on different strategies for pivoting: partial pivoting, incremental pivoting, and tournament pivoting. The fourth one replaces pivoting with the Partial Random Butterfly Transformation, and finally, an implementation without pivoting is used as a performance baseline. The technique of iterative refinement is applied to recover numerical accuracy when necessary. All parallel implementations are produced using dynamic, superscalar, runtime scheduling and tile matrix layout. Results on two multisocket multicore systems are presented. Performance and numerical accuracy is analyzed. Copyright © 2014 John Wiley & Sons, Ltd.

A 15-point high-order compact scheme with multigrid computation for solving 3D convection diffusion equations

We propose a method with sixth-order accuracy to solve the three-dimensional (3D) convection diffusion equation. We first use a 15-point fourth-order compact discretization scheme to obtain fourth-order solutions on both fine and coarse grids using the multigrid method. Then an iterative mesh refinement technique combined with Richardson extrapolation is used to approximate the sixth-order accurate solution on the fine grid. Numerical results are presented for a variety of test cases to demonstrate the efficiency and accuracy of the proposed method, compared with the standard fourth-order compact scheme.

Real-Time Stereo Matching on CUDA Using an Iterative Refinement Method for Adaptive Support-Weight Correspondences

High-quality real-time stereo matching has the potential to enable various computer vision applications including semi-automated robotic surgery, teleimmersion, and 3-D video surveillance. A novel real-time stereo matching method is presented that uses a two-pass approximation of adaptive support-weight aggregation, and a low-complexity iterative disparity refinement technique. Through an evaluation of computationally efficient approaches to adaptive support-weight cost aggregation, it is shown that the two-pass method produces an accurate approximation of the support weights while greatly reducing the complexity of aggregation. The refinement technique, constructed using a probabilistic framework, incorporates an additive term into matching cost minimization and facilitates iterative processing to improve the accuracy of the disparity map. This method has been implemented on massively parallel high-performance graphics hardware using the Compute Unified Device Architecture computing engine. Results show that the proposed method is the most accurate among all of the real-time stereo matching methods listed on the Middlebury stereo benchmark.

An Analytical Placer for VLSI Standard Cell Placement

Placement is the process of determining the exact locations of circuit elements within a chip. It is a crucial step in very large scale integration (VLSI) physical design, because it affects routability, performance, and power consumption of a design. In this paper, we develop a new analytical placer to solve the VLSI standard cell placement problem. The placer consists of two phases, multilevel global placement (GP) and detailed cell placement (DP). In the stage of GP, during the clustering stage, we use a nonlinear programming technique and a best-choice clustering algorithm to take a global view of the whole netlist and placement information, and then use an iterative local refinement technique during the declustering stage to further distribute the cells and reduce the wirelength. In the stage of DP, we develop a fast legalization algorithm to make the solution by global placement legal and use a cell order polishing to improve the legal solution. The proposed algorithm is tested on the IBM standard cell benchmark circuits and Peko suites. Experimental results show that our placer obtains high-quality results in a reasonable running time.

Comprehensive comparison of graph based multiple protein sequence alignment strategies

BackgroundAlignment of protein sequences (MPSA) is the starting point for a multitude of applications in molecular biology. Here, we present a novel MPSA program based on the SeqAn sequence alignment library. Our implementation has a strict modular structure, which allows to swap different components of the alignment process and, thus, to investigate their contribution to the alignment quality and computation time. We systematically varied information sources, guiding trees, score transformations and iterative refinement options, and evaluated the resulting alignments on BAliBASE and SABmark.ResultsOur results indicate the optimal alignment strategy based on the choices compared. First, we show that pairwise global and local alignments contain sufficient information to construct a high quality multiple alignment. Second, single linkage clustering is almost invariably the best algorithm to build a guiding tree for progressive alignment. Third, triplet library extension, with introduction of new edges, is the most efficient consistency transformation of those compared. Alternatively, one can apply tree dependent partitioning as a post processing step, which was shown to be comparable with the best consistency transformation in both time and accuracy. Finally, propagating information beyond four transitive links introduces more noise than signal.ConclusionsThis is the first time multiple protein alignment strategies are comprehensively and clearly compared using a single implementation platform. In particular, we showed which of the existing consistency transformations and iterative refinement techniques are the most valid. Our implementation is freely available at http://ekhidna.biocenter.helsinki.fi/MMSA and as a supplementary file attached to this article (see Additional file 1).

Iterative refinement techniques for solving block linear systems of equations

We study the numerical properties of classical iterative refinement (IR) and k-fold iterative refinement (RIR) for computing the solution of a nonsingular linear system of equations Ax=b with A partitioned into blocks using floating point arithmetic. We assume that all computations are performed in the working (fixed) precision. We prove that the numerical quality of RIR is superior to that of IR.

Scaling abstraction refinement via pruning

Many static analyses do not scale as they are made more precise. For example, increasing the amount of context sensitivity in a k -limited pointer analysis causes the number of contexts to grow exponentially with k . Iterative refinement techniques can mitigate this growth by starting with a coarse abstraction and only refining parts of the abstraction that are deemed relevant with respect to a given client. In this paper, we introduce a new technique called pruning that uses client feedback in a different way. The basic idea is to use coarse abstractions to prune away parts of the program analysis deemed irrelevant for proving a client query, and then using finer abstractions on the sliced program analysis. For a k -limited pointer analysis, this approach amounts to adaptively refining and pruning a set of prefix patterns representing the contexts relevant for the client. By pruning, we are able to scale up to much more expensive abstractions than before. We also prove that the pruned analysis is both sound and complete, that is, it yields the same results as an analysis that uses a more expensive abstraction directly without pruning.

Error concealment for motion-compensated interpolation

Motion-compensated interpolation is usually employed at the receiver end in order to improve the quality of the video, when a low-bit-rate video is encoded in conjunction with frame dropping. The authors propose a scheme that can exploit the block-based motion vector field available at the decoder to avoid the complex motion estimation. The scheme is based on an iterative refinement technique that employs the finite-element method to efficiently conceal the interpolation errors caused by unfilled holes or overlapped pixels in the predicted frames. As a consequence, no pixel classification is needed in the proposed scheme, thus reducing substantially the computational complexity. The scheme is capable of concealing the errors in the homogeneous regions as well as in regions containing sharp edges. The proposed scheme is simulated with the original frames of a number of test sequences, as well as implemented with the H.264/AVC decoded frames. The results from these extensive simulations show that the proposed scheme results in reconstructed frames having a better visual quality and a lower computational complexity than the existing schemes.

O.071 Magnetic field interactions in adjustable hydrocephalus shunts

Panoramic line-scan cameras provide high definition images with a quasi uniform distribution of the sensing elements. Unfortunately, calibration of such devices with classic techniques is not possible making their use, in computer vision field, not straightforward. We propose a flexible and convenient calibration method for the computation of intrinsic and mechanism parameters of such systems by using images of a simple calibration pattern. Unlike existing approaches, the proposed method considers a full geometrical model and does not make any unattainable assumption such as concentricity of images, a priori knowledges about camera poses or coincidence of the rotation axis with the optical center. Using few images taken with free poses, the calibration is performed in two steps. First, the intrinsic parameters are computed using sets of 2D/3D point correspondences that are generated automatically by exploiting the structure of the calibration rig. Then, thanks to the parameterization of the projection of a 3D straight line, the mechanical parameters are computed using points at infinity. For each step, closed form solutions and iterative refinement techniques are presented. The proposed approach is validated with both synthetic and real data collected by our prototype.

Solving Systems of Linear Equations on the CELL Processor Using Cholesky Factorization

The Sony/Toshiba/IBM (STI) CELL processor introduces pioneering solutions in processor architecture. At the same time it presents new challenges for the development of numerical algorithms. One is effective exploitation of the differential between the speed of single and double precision arithmetic; the other is efficient parallelization between the short vector SIMD cores. The first challenge is addressed by utilizing the well known technique of iterative refinement for the solution of a dense symmetric positive definite system of linear equations, resulting in a mixed-precision algorithm, which delivers double precision accuracy, while performing the bulk of the work in single precision. The main contribution of this paper lies in addressing the second challenge by successful thread-level parallelization, exploiting fine-grained task granularity and a lightweight decentralized synchronization. The implementation of the computationally intensive sections gets within 90 percent of peak floating point performance, while the implementation of the memory intensive sections reaches within 90 percent of peak memory bandwidth. On a single CELL processor, the algorithm achieves over 170~Gflop/s when solving a symmetric positive definite system of linear equation in single precision and over 150~Gflop/s when delivering the result in double precision accuracy.