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The error control of local interpolation for a 2D MLFMA will be discussed. The way to select proper parameters is proposed in terms of both numerical accuracy and computational cost. Satisfying the conditions derived in this paper, error can be controlled at the same level as global interpolation, and the computational cost becomes less expensive than the global one. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 36: 8–12, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10655 [ABSTRACT FROM AUTHOR]

Summary: This paper focuses on designing and implementing parallel Moving Least Squares (MLS) interpolation algorithms by exploiting the Graphics Processing Unit (GPU) for the usage in Meshfree methods. The MLS method is an approach for scattered points' approximation / interpolation, which is commonly employed as the shape functions in various Meshfree methods. To improve the computational efficiency in building stiffness matrices in Meshfree methods, we are specifically interested in parallelizing the MLS interpolation on the GPU. The accelerated Meshfree methods can be employed to numerically analyze large deformations of soil and rock masses such as the landslides. In this paper, we first introduce our previously proposed method for finding the k nearest neighboring points located within the local region of the interest point in MLS. We then develop one sequential and three parallel implementations for each of three variations of the MLS interpolation, including the serial implementation, the parallel implementation on the multi‐core CPU, the parallel implementation on a single GPU, and the parallel implementation on multi‐GPUs. To evaluate the computational performance of our GPU implementations, five groups of benchmark tests are conducted in both two‐dimensions and three‐dimensions. We observe that our GPU implementations can achieve satisfied speedups over the sequential CPU implementation for varied sizes of testing data. To benefit the community, all source code and testing data related to the presented parallel MLS interpolation are publicly available. [ABSTRACT FROM AUTHOR]

Despite the large amount of work devoted in recent years to the problem of non-rigid shape matching, practical methods that can successfully be used for arbitrary pairs of shapes remain elusive. In this paper, we study the hardness of the problem of shape matching, and introduce the notion of the shape condition number, which captures the intuition that some shapes are inherently more difficult to match against than others. In particular, we make a connection between the symmetry of a given shape and the stability of any method used to match it while optimizing a given distortion measure. We analyze two commonly used classes of methods in deformable shape matching, and show that the stability of both types of techniques can be captured by the appropriate notion of a condition number. We also provide a practical way to estimate the shape condition number and show how it can be used to guide the selection of landmark correspondences between shapes. Thus we shed some light on the reasons why general shape matching remains difficult and provide a way to detect and mitigate such difficulties in practice. [ABSTRACT FROM AUTHOR]

Algebraic multigrid (AMG) is one of the most efficient and scalable parallel algorithms for solving sparse linear systems on unstructured grids. However, for large 3D problems, the coarse grids that are normally used in AMG often lead to growing complexity in terms of memory use and execution time per AMG V-cycle. Sparser coarse grids, such as those obtained by the parallel modified independent set (PMIS) coarsening algorithm, remedy this complexity growth but lead to nonscalable AMG convergence factors when traditional distance-one interpolation methods are used. In this paper, we study the scalability of AMG methods that combine PMIS coarse grids with long-distance interpolation methods. AMG performance and scalability are compared for previously introduced interpolation methods as well as new variants of them for a variety of relevant test problems on parallel computers. It is shown that the increased interpolation accuracy largely restores the scalability of AMG convergence factors for PMIS-coarsened grids, and in combination with complexity reducing methods, such as interpolation truncation, one obtains a class of parallel AMG methods that enjoy excellent scalability properties on large parallel computers. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The translation matrix for the multilevel fast multipole algorithm (MLFMA) in an FISC (fast Illinois solver code) is calculated directly, and the complexity is O(N3/2), where N is the number of unknowns. For a problem with a small electrical size, the CPU time for calculating the translation matrix can be negligible. But for large problems, the calculation time increases significantly. In this paper, we use interpolation to calculate the translation matrix, and the complexity is reduced to O(N). Different interpolation techniques are tested, and it is found that the Lagrange polynomial interpolation with high sampling rates is the best. The saving factor is 10 for the VFY218 at 4 GHz. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 30: 109–114, 2001. [ABSTRACT FROM AUTHOR]

Given convex scattered data in R3 we consider the constrained interpolation problem of finding a smooth, minimal Lp-norm (1 < p < ∞) interpolation network that is convex along the edges of an associated triangulation. In previous work the problem has been reduced to the solution of a nonlinear system of equations. In this paper we formulate and analyse a Newton-type algorithm for solving the corresponding type of systems. The correctness of the application of the proposed method is proved and its superlinear (in some cases quadratic) convergence is shown. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The application of the FDTD algorithm on generalized non-orthogonal meshes, following the basic ideas of Holland (1983), has been investigated by many authors for several years now, and detailed dispersion analysis as well as convergence studies have been published. Already in 1992 also a general stability criterion was given for the time integration using the standard leap-frog scheme (Lee et al.). Many authors, however, still propose some damped time stepping algorithms to work around unexpected instabilities in the discretization method. In this paper the origin of this type of instability is revealed, and a technique to obtain a stable discretization of Maxwell’s equations on non-orthogonal grids is proposed. To obtain more insight into the stability properties of the method, it is reformulated according to the matrix–vector notation of the Finite Integration Technique. © 1998 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We present physically based algorithms for interactive deformable shape and motion modelling. We coarsely sample the objects with simulation nodes, and apply a meshless finite element method to obtain realistic deformations at interactive frame rates. This shape deformation algorithm is then used to specify keyframe poses and a smooth interpolating motion is obtained by solving for an energy-minimizing trajectory. We show how to handle collisions between different deformable objects as well as with static or moving scene objects. Secondary motion is added as a post-process by running a meshless elastic solid simulation. We enforce precomputed trajectories using control forces computed using shape matching. Key to the efficiency of our method is a sparse deformation representation and an adaptive optimization algorithm that automatically introduces new degrees of freedom in problematic regions. An accurate temporal interpolation scheme that exactly recovers rigid motions keeps the number of unknowns low and achieves realistic deformations with very few keyframes. We also show how the algorithm allows combining purely physical simulation with keyframe-based scripted animation. The presented results illustrate that our framework can handle complex shapes at interactive rates, making it a valuable tool for animators to realistically model deformable 3D shapes and their motion. [ABSTRACT FROM AUTHOR]

Recently, a new type of time step integration algorithms using complex time steps has been proposed. For linear problems, the algorithms are higher order accurate, unconditionally stable and have directly controllable numerical dissipation. Solutions with high accuracy can be generated using large time steps. In this paper, the algorithms are extended to solve non-linear problems. The pseudo-force approach is adopted in treating the non-linear terms. To maintain the solutions accuracy, the pseudo-force is reconstructed by interpolation. Special treatments are required to compute the excitation at the complex time steps. Several numerical examples are analysed. It is observed that the complex time step method can be computationally more efficient than the Newmark method when very accurate numerical solutions are required. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Sleep spindle brain waves have an important role in the sleeping mechanism. Recently, computer-aided automatic analysis methods have been introduced in the form of numerical analysis of frequency, duration, etc., and their rapid progress has been noted. However, the spindle waves are transient nonstationary "phasic events," and therefore their accurate frequency analysis has caused serious difficulties. Aiming at the accurate frequency analysis of the spindle waves, the authors have already proposed an analysis algorithm based on complex demodulation (CD) in the time domain, but the long processing time required for the analysis has remained a problem. This paper proposes a new analysis algorithms which combines the advantage of frequency domain CD and Hilbert transformation mainly to speed up the measurement of instantaneous amplitude and, in the case of measuring the instantaneous frequency, the advantage of the Cd method using interpolation is exploited to improve the accuracy. Here, the proposed method is explained concretely and the analysis results are investigated in comparison with the time domain CD method published earlier. [ABSTRACT FROM AUTHOR]

Summary: The estimation of finite‐horizon discrete‐choice dynamic programming (DCDP) models is computationally expensive. This limits their realism and impedes verification and validation efforts. Keane and Wolpin (Review of Economics and Statistics, 1994, 76(4), 648–672) propose an interpolation method that ameliorates the computational burden but introduces approximation error. I describe their approach in detail, successfully recompute their original quality diagnostics, and provide some additional insights that underscore the trade‐off between computation time and the accuracy of estimation results. [ABSTRACT FROM AUTHOR]

The phase-shift-plus-interpolation and extended-split-step-Fourier methods are wavefield-continuation algorithms for seismic migration imaging. These two methods can be applied to regions with complex geological structures. Based on their unified separable formulas, we show that these two methods have the same kinematic characteristics by using the theory of pseudodifferential operators. Numerical tests on a Marmousi model demonstrate this conclusion. Another important aspect of these two methods is the selection of reference velocities and we explore the influence of the selection of reference velocities by comparing the geometric progression method and the statistical method. We show that the geometric progression method is simple but does not take into account the velocity distribution while the statistical approach is relatively complex but reflects the velocity distribution. [ABSTRACT FROM AUTHOR]

We extend the rendering technique for continuous scatterplots to allow for a broad class of interpolation methods within the spatial grid instead of only linear interpolation. To do this, we propose an approach that projects the image of a cell from the spatial domain to the scatterplot domain. We approximate this image using either the convex hull or an axis-aligned rectangle that forms a tight fit of the projected points. In both cases, the approach relies on subdivision in the spatial domain to control the approximation error introduced in the scatterplot domain. Acceleration of this algorithm in homogeneous regions of the spatial domain is achieved using an octree hierarchy. The algorithm is scalable and adaptive since it allows us to balance computation time and scatterplot quality. We evaluate and discuss the results with respect to accuracy and computational speed. Our methods are applied to examples of 2-D transfer function design. [ABSTRACT FROM AUTHOR]

Bai et al. recently proposed to acquire random fan-beam/cone-beam projections with a linear/planar detector from a circular scanning locus for controlled cardiac computed tomography (CT). After specifying a uniform acquisition geometry required by FBP (filtration-backprojection), we rebin the random fan-beam/cone-beam data via nearest-neighbor, quadrilateral and triangle-based linear interpolation methods. The fan-beam and parallel-beam FBP algorithms are employed for rebinned fan-beam projections. The FDK (Feldkamp–Davis–Kress) and t-FDK (tent-FDK) methods are employed for rebinned cone-beam data. Also, nonuniform weighting fan-beam/FDK methods are used to reconstruct without rebinning. As a benchmark, the images are reconstructed using uniform weighting fan-beam/FDK method from data collected at the specified uniform grid. To evaluate the different methods, effects of increasing the number of projections and adding Poisson noise are studied. The root mean square error (RMSE) is used to quantify the image quality by numerical tests with the cardiac phantom. Our results show that it is helpful to perform data interpolation for improvements of the image quality in controlled cardiac CT from random projections. Our simulations indicate that triangular interpolation gives the most satisfactory result for improved image quality whereas quadrilateral interpolationgives the best noise performance. © 2007 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 17, 91–98, 2007 [ABSTRACT FROM AUTHOR]

This study presents the application of fast spherical transforms developed by Driscoll and Healy (Adv Appl Math 15 (1994), 202–250) to the full-wave multilevel fast multipole method. An accurate uniform-grid based quadrature rule is presented, along with fast algorithms for interpolation and anterpolation. Error behavior and algorithmic complexities are discussed. Finally an efficient method for the generation of translation operators is presented. The overall method results in efficient and error-controllable schemes for quadrature and interpolation. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 1961–1964, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21825 [ABSTRACT FROM AUTHOR]

We propose the concept of a latent doodle space, a low-dimensional space derived from a set of input doodles, or simple line drawings. The latent space provides a foundation for generating new drawings that are similar, but not identical to, the input examples. The two key components of this technique are 1) a heuristic algorithm for finding stroke correspondences between the drawings, and 2) the use of latent variable methods to automatically extract a low-dimensional latent doodle space from the inputs. We present two practical applications that demonstrate the utility of this idea: first, a randomized stamp tool that creates a different image on every usage; and second, “personalized probabilistic fonts,” a handwriting synthesis technique that mimics the idiosyncrasies of one's own handwriting. Keywords: sketch, by-example, style learning, scattered data interpolation, principal component analysis, radial basis functions, Gaussian processes, digital in-betweening, handwriting synthesis [ABSTRACT FROM AUTHOR]

In order to solve hyperbolic partial differential equations by means of the Interpolated Differential Operator (IDO) scheme, time integration of the dependent variable has been carried out by Taylor expansion, and time differentiation has been performed by replacing it with a spatial differentiation. However, in such a method, the time accuracy is limited by the order of the interpolation function and in addition the spatial accuracy is not sufficient in multidimensional problems due to the complexity of the calculations. In terms of numerical stability, the stable region indicated by the CFL (Courant-Friedrich-Levy) number is narrow. Hence, in order to improve the space-time accuracy and to secure numerical stability, time integration by the Runge-Kutta method is applied. Further, a method for increasing the order of the Runge-Kutta method without increasing the computational cost is proposed, taking advantage of the characteristics of the IDO scheme with the physical quantity and its spatial derivative as the dependent variables. The two-dimensional advection equation and the one-dimensional wave equation are solved and the results are quantitatively compared with those obtained by the conventional Taylor expansion. Also, in order to demonstrate the adaptability of this approach to practical problems, we consider Williamson's test case 5 for the shallow-water equation in spherical geometry. It is found that the Runge-Kutta method for multiple dimensions yields accuracy and stability higher than those of the Taylor expansion, demonstrating the effectiveness of the approach. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 87(2): 33–42, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10127 [ABSTRACT FROM AUTHOR]

It is known that the glottal waveform includes acoustic information on the individuality of speakers, and that the inverse filtering method is useful in extracting glottal waveform from speech signals. In conventional methods, stationary analysis is performed for the duration of a few pitches. Short-time analysis with the drawback of unstable estimation, is performed for one pitch duration. We propose a new method of inverse filtering by using the estimation algorithm for the vocal tract transfer function; the analysis is performed stably for each pitch using the mapping algorithm with the Fejér kernel. The experimental results show reasonable estimation of glottal waveforms. In addition, we investigate the effect of the estimation order and the method of solving the Yule-Walker equation. The experiments are performed for (1) different speakers, and different vowels in different order, and (2) different algorithms such as the TLS and Levinson algorithm. © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 82(2): 28–36, 1999 [ABSTRACT FROM AUTHOR]