scholarly journals On Solving Pentadiagonal Linear Systems via Transformations

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
S. S. Askar ◽  
A. A. Karawia
Keyword(s):  
Linear Systems ◽  
Computational Cost ◽  
Numerical Algorithms ◽  
Current Paper ◽  
Better Than ◽  
Symbolic Algorithms

Many authors have studied numerical algorithms for solving the linear systems of pentadiagonal type. The well-known fast pentadiagonal system solver algorithm is an example of such algorithms. The current paper describes new numerical and symbolic algorithms for solving pentadiagonal linear systems via transformations. The proposed algorithms generalize the algorithms presented in El-Mikkawy and Atlan, 2014. Our symbolic algorithms remove the cases where the numerical algorithms fail. The computational cost of our algorithms is better than those algorithms in literature. Some examples are given in order to illustrate the effectiveness of the proposed algorithms. All experiments are carried out on a computer with the aid of programs written in MATLAB.

The Met Office operational global ocean forecast system FOAM-ORCA12

2021 ◽  
Author(s):  
Ana Barbosa Aguiar ◽  
Jennifer Waters ◽  
Martin Price ◽  
Gordon Inverarity ◽  
Christine Pequignet ◽  
...  
Keyword(s):  
Computational Cost ◽  
Absolute Error ◽  
Global Ocean ◽  
Background Error ◽  
Verification Methods ◽  
Climate Simulations ◽  
Forecast Models ◽  
The Mean ◽  
Lower Continuous ◽  
Better Than

<div> <p>The importance of oceans for atmospheric forecasts as well as climate simulations is being increasingly recognised with the advent of coupled ocean / atmosphere forecast models. Having comparable resolutions in both domains maximises the benefits for a given computational cost. The Met Office has recently upgraded its operational global ocean-only model from an eddy permitting 1/4 degree tripolar grid (ORCA025) to the eddy resolving 1/12 degree ORCA12 configuration while retaining 1/4 degree data assimilation. </p> </div><div> <p>We will present a description of the ocean-only ORCA12 system, FOAM-ORCA12, alongside some initial results. Qualitatively, FOAM-ORCA12 seems to represent better (than FOAM-ORCA025) the details of mesoscale features in SST and surface currents. Overall, traditional statistical results suggest that the new FOAM-ORCA12 system performs similarly or slightly worse than the pre-existing FOAM-ORCA025. However, it is known that comparisons of models running at different resolutions suffer from a double penalty effect, whereby higher-resolution models are penalised more than lower-resolution models for features that are offset in time and space. Neighbourhood verification methods seek to make a fairer comparison using a common spatial scale for both models and it can be seen that, as neighbourhood sizes increase, ORCA12 consistently has lower continuous ranked probability scores (CRPS) than ORCA025. CRPS measures the accuracy of the pseudo-ensemble created by the neighbourhood method and generalises the mean absolute error measure for deterministic forecasts. </p> </div><div> <p>The focus over the next year will be on diagnosing the performance of both the model and assimilation. A planned development that is expected to enhance the system is the update of the background-error covariances used for data assimilation. </p> </div>

scholarly journals A competitive comparison of multiparameter stacking operators

Geophysics ◽  
2017 ◽  
Vol 82 (4) ◽  
pp. V275-V283 ◽  
Author(s):  
Jan Walda ◽  
Benjamin Schwarz ◽  
Dirk Gajewski
Keyword(s):  
Optimization Technique ◽  
Computational Cost ◽  
Initial Guess ◽  
Time Shift ◽  
Data Set ◽  
Velocity Shift ◽  
Common Reflection Surface ◽  
The One ◽  
Better Than ◽  
Good Agreement

The classic common-midpoint (CMP) stack, which sums along offsets, suffers in challenging environments in which the acquisition is sparse. In the past, several multiparameter stacking techniques were introduced that incorporate many neighboring CMPs during summation. This increases data redundancy and reduces noise. Multiparameter methods that can be parameterized by the same wavefront attributes are multifocusing (MF), the common-reflection-surface (CRS), implicit CRS, and nonhyperbolic CRS (nCRS). The CRS-type operators use a velocity-shift mechanism to account for heterogeneity by changing the slope of the asymptote. On the other hand, MF uses a different mechanism: a shift of reference time while preserving the slope of the asymptote. We have formulated MF such that it uses the same mechanism as the CRS-type operators and compare them on a marine data set. In turn, we investigate the behavior of time-shifted versions of the CRS-type approximations. To provide a fair comparison, we use a global optimization technique, differential evolution, which allows to accurately estimate a solution without an initial guess solution. Our results indicate that the velocity-shift mechanism performs, in general, better than the one incorporating a time shift. The double-square-root operators are also less sensitive to the choice of aperture. They perform better in the case of diffractions than conventional hyperbolic CRS, and this fact is in good agreement with previous works. In our work the nCRS is of almost the same computational cost as that of conventional hyperbolic CRS, but it generally leads to a superior fit; therefore, we recommend its use in the future.

scholarly journals On the Hardness of Offline Multi-objective Optimization

2007 ◽  
Vol 15 (4) ◽  
pp. 475-491 ◽  
Author(s):  
Olivier Teytaud
Keyword(s):  
Evolutionary Algorithms ◽  
Convergence Rate ◽  
Random Search ◽  
Computational Cost ◽  
Multiobjective Evolutionary Algorithms ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Conflicting Objectives ◽  
Insight Into ◽  
Better Than

It has been empirically established that multiobjective evolutionary algorithms do not scale well with the number of conflicting objectives. This paper shows that the convergence rate of all comparison-based multi-objective algorithms, for the Hausdorff distance, is not much better than the convergence rate of the random search under certain conditions. The number of objectives must be very moderate and the framework should hold the following assumptions: the objectives are conflicting and the computational cost is lower bounded by the number of comparisons is a good model. Our conclusions are: (i) the number of conflicting objectives is relevant (ii) the criteria based on comparisons with random-search for multi-objective optimization is also relevant (iii) having more than 3-objectives optimization is very hard. Furthermore, we provide some insight into cross-over operators.

scholarly journals Statistical applications for equivariant matrices

2001 ◽  
Vol 25 (1) ◽  
pp. 53-61
Author(s):  
S. H. Alkarni
Keyword(s):  
Linear Systems ◽  
Fourier Transforms ◽  
Toeplitz Matrices ◽  
Computational Cost ◽  
Special Kind ◽  
Circulant Matrices ◽  
Stationary Processes ◽  
Linear System Of Equations ◽  
The Matrix ◽  
A Finite Group

Solving linear system of equationsAx=benters into many scientific applications. In this paper, we consider a special kind of linear systems, the matrixAis an equivariant matrix with respect to a finite group of permutations. Examples of this kind are special Toeplitz matrices, circulant matrices, and others. The equivariance property ofAmay be used to reduce the cost of computation for solving linear systems. We will show that the quadratic form is invariant with respect to a permutation matrix. This helps to know the multiplicity of eigenvalues of a matrix and yields corresponding eigenvectors at a low computational cost. Applications for such systems from the area of statistics will be presented. These include Fourier transforms on a symmetric group as part of statistical analysis of rankings in an election, spectral analysis in stationary processes, prediction of stationary processes and Yule-Walker equations and parameter estimation for autoregressive processes.

scholarly journals (2n-1)-Point Ternary Approximating and Interpolating Subdivision Schemes

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Muhammad Aslam ◽  
Ghulam Mustafa ◽  
Abdul Ghaffar
Keyword(s):  
Explicit Formula ◽  
Error Bounds ◽  
Computational Cost ◽  
Subdivision Schemes ◽  
Special Cases ◽  
Better Than

We present an explicit formula which unifies the mask of(2n-1)-point ternary interpolating as well as approximating subdivision schemes. We observe that the odd point ternary interpolating and approximating schemes introduced by Lian (2009), Siddiqi and Rehan (2010, 2009) and Hassan and Dodgson (2003) are special cases of our proposed masks/schemes. Moreover, schemes introduced by Zheng et al. (2009) can easily be generated by our proposed masks. It is also proved from comparison that(2n-1)-point schemes are better than2n-scheme in the sense of computational cost, support and error bounds.

Parallel Solution of Linear Systems

2016 ◽  
Vol 6 (3) ◽  
pp. 278-289
Author(s):  
Sidi-Mahmoud Kaber ◽  
Amine Loumi ◽  
Philippe Parnaudeau
Keyword(s):  
Linear Systems ◽  
Numerical Algorithms ◽  
Parallel Architecture ◽  
Decomposition Methods ◽  
Partial Fraction ◽  
Domain Decomposition Methods ◽  
Simple Method ◽  
Parallel Solution ◽  
Partial Fraction Decomposition ◽  
Programming Paradigms

AbstractComputational scientists generally seek more accurate results in shorter times, and to achieve this a knowledge of evolving programming paradigms and hardware is important. In particular, optimising solvers for linear systems is a major challenge in scientific computation, and numerical algorithms must be modified or new ones created to fully use the parallel architecture of new computers. Parallel space discretisation solvers for Partial Differential Equations (PDE) such as Domain Decomposition Methods (DDM) are efficient and well documented. At first glance, parallelisation seems to be inconsistent with inherently sequential time evolution, but parallelisation is not limited to space directions. In this article, we present a new and simple method for time parallelisation, based on partial fraction decomposition of the inverse of some special matrices. We discuss its application to the heat equation and some limitations, in associated numerical experiments.

scholarly journals A Modified SSOR Preconditioning Strategy for Helmholtz Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Shi-Liang Wu ◽  
Cui-Xia Li
Keyword(s):  
Convergence Rate ◽  
Linear Systems ◽  
Iterative Methods ◽  
Low Cost ◽  
Computational Cost ◽  
Coefficient Matrix ◽  
Computational Time ◽  
Helmholtz Equations ◽  
Speed Up ◽  
Methods Numerical

The finite difference method discretization of Helmholtz equations usually leads to the large spare linear systems. Since the coefficient matrix is frequently indefinite, it is difficult to solve iteratively. In this paper, a modified symmetric successive overrelaxation (MSSOR) preconditioning strategy is constructed based on the coefficient matrix and employed to speed up the convergence rate of iterative methods. The idea is to increase the values of diagonal elements of the coefficient matrix to obtain better preconditioners for the original linear systems. Compared with SSOR preconditioner, MSSOR preconditioner has no additional computational cost to improve the convergence rate of iterative methods. Numerical results demonstrate that this method can reduce both the number of iterations and the computational time significantly with low cost for construction and implementation of preconditioners.

scholarly journals Rejection Sampling Schemes for Simulating from Arbitrary Probability Densities

2020 ◽  
Vol 68 (1) ◽  
pp. 59-64
Author(s):  
Anamul Haque Sajib
Keyword(s):  
Monte Carlo ◽  
Computational Cost ◽  
The Other ◽  
Rejection Sampling ◽  
Mcmc Method ◽  
Empirical Comparison ◽  
Sampling Schemes ◽  
Probability Densities ◽  
Better Than

Simulating random variates from arbitrary non-normalized probability densities, very often they do not have familiar forms, is an increasingly important requirement in many different fields, especially in Bayesian statistics. Accept-reject algorithm is one of the commonly used methods to simulate random variates from such densities but restriction on choosing proposal density under this framework (heavier tails than the target density) limits its applicability to a larger extent. On the other hand, Markov Chain Monte Carlo (MCMC) method can choose proposal density arbitrary which makes this method applicable to a larger class of target densities5. In addition to MCMC method, a more general widely used method known as ratio-of-uniforms (RoU) which requires only two uniform variates to simulate one variates from such densities. However, no empirical comparison among these methods for simulating random variates from such densities was seen in the literature. In this paper, we limit our study only to MCMC and RoU methods to simulate random variates from such densities. Following the generation of random variates from such densities using these two methods, we compare the performance of these two methods based on quality of the generated samples. Finally, we conclude that RoU method performs better than MCMC method as far as quality of the generated sample (randomness) and computational cost are concerned. Dhaka Univ. J. Sci. 68(1): 59-64, 2020 (January)

scholarly journals A Comparative Study of Water Indexes and Image Classification Algorithms for Mapping Inland Surface Water Bodies Using Landsat Imagery

2019 ◽  
Author(s):  
Feifei Pan ◽  
Xiaohuan Xi ◽  
Cheng Wang
Keyword(s):  
Image Classification ◽  
Landsat Imagery ◽  
Red Light ◽  
Computational Cost ◽  
Google Earth ◽  
Classification Algorithms ◽  
Landsat 8 ◽  
Water Index ◽  
Otsu Method ◽  
Better Than

To address three important issues related to extraction of water features from Landsat imagery, i.e., selection of water indexes and classification algorithms for image classification, collection of ground truth data for accuracy assessment, this study applied four sets (ultra-blue, blue, green, and red light based) of water indexes (NWDI, MNDWI, MNDWI2, AWEIns, and AWEIs) combined with three types of image classification methods (zero-water index threshold, Otsu, and kNN) to 24 selected lakes across the globe to extract water features from Landsat-8 OLI imagery. 1440 (4x5x3x24) image classification results were compared with the extracted water features from high resolution Google Earth images with the same (or ±1 day) acquisition dates through computing the Kappa coefficients. Results show the kNN method is better than the Otsu method, and the Otsu method is better than the zero-water index threshold method. If the computational cost is not an issue, the kNN method combined with the ultra-blue light based AWEIns is the best method for extracting water features from Landsat imagery because it produced the highest Kappa coefficients. If the computational cost is taken into account, the Otsu method is a good choice. AWEIns and AWEIs are better than NDWI, MNDWI and MNDWI2. AWEIns works better than AWEIs under the Otsu method, and the average rank of the image classification accuracy from high to low is the ultra-blue, blue, green, and red light-based AWEIns.

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