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A sixth-order iterative method for approximating the polar decomposition of an arbitrary matrix

Alicia Cordero, Juan R. Torregrosa
2017 Journal of Computational and Applied Mathematics  
A sixth-order iterative method for approximating the polar decomposition of an arbitrary matrix. Journal of Computational and Applied Mathematics. 318:591-598.  ...  Abstract A new iterative method for computing the polar decomposition of any rectangular complex matrix is presented and analyzed.  ...  In this paper, we have proposed and iterative method, for approximating the polar decomposition of an arbitrary complex matrix, with order of convergence six.  ... 
doi:10.1016/j.cam.2015.12.006 fatcat:3iwonbkukrhqxalefbogzliyqa

A Novel Iterative Method for Polar Decomposition and Matrix Sign Function

F. Soleymani, Predrag S. Stanimirović, Igor Stojanović
2015 Discrete Dynamics in Nature and Society  
We define and investigate a globally convergent iterative method possessing sixth order of convergence which is intended to calculate the polar decomposition and the matrix sign function.  ...  Some analysis of stability and computational complexity are brought forward. The behaviors of the proposed algorithms are illustrated by numerical experiments.  ...  The second and third authors gratefully acknowledge support from the Project "Applying Direct Methods for Digital Image Restoring" of the Goce Delc ev University.  ... 
doi:10.1155/2015/649423 fatcat:yw3zhyzdd5dlzn2o66dpfxo3mu

Several numerical methods for computing unitary polar factor of a matrix

Fazlollah Soleymani, Farhad Khaksar Haghani, Stanford Shateyi
2016 Advances in Difference Equations  
We present several numerical schemes for computing the unitary polar factor of rectangular complex matrices. Error analysis shows high orders of convergence.  ...  Many experiments in terms of number of iterations and elapsed times are reported to show the efficiency of the new methods in contrast to the existing ones. MSC: 65F30  ...  Acknowledgements The authors thank the anonymous referees for their suggestions which helped to improve the quality of the paper.  ... 
doi:10.1186/s13662-015-0732-z fatcat:q3fbsm3turgnvovwexnoeetoja

Real and Complex Dynamics of Iterative Methods

Alicia Cordero, Juan R. Torregrosa, Beny Neta, Taher Lotfi
2016 Discrete Dynamics in Nature and Society  
In the recent years, the study of the dynamical behavior of the rational operator associated with an iterative method has become a rapidly growing area of research, since the dynamical properties of the  ...  Although the main aims of the construction of iterative schemes are to get high order of convergence and computational efficiency, their stability is an important subject to be taken into account: the  ...  Acknowledgments The guest editors would like to express their gratitude to all researchers who submitted papers for publication and to the many reviewers whose reports were essential for them.  ... 
doi:10.1155/2016/4765286 fatcat:2dl3n4dcofbgxojmo2qszdbagy

Efficient Computation of Slepian Functions for Arbitrary Regions on the Sphere

Alice P. Bates, Zubair Khalid, Rodney A. Kennedy
2017 IEEE Transactions on Signal Processing  
By exploiting the efficient computation of Slepian functions for the polar cap region on the sphere, we develop a formulation, supported by a fast algorithm, for the approximate computation of Slepian  ...  For the special case of a polar cap, the symmetry of the region enables the decomposition of the Slepian concentration problem into smaller subproblems and consequently the efficient computation of Slepian  ...  CONCLUSIONS We have proposed a new method for the computation of Slepian functions on the sphere for an arbitrary spatial region.  ... 
doi:10.1109/tsp.2017.2712122 fatcat:aye3pwckcnde5pt35ngkagkbci

High-order symplectic Lie group methods on $ SO(n) $ using the polar decomposition

Xuefeng Shen, Khoa Tran, Melvin Leok
2022 Journal of Computational Dynamics  
> is constructed using the polar decomposition and the constrained Galerkin method.  ...  It has the advantage of avoiding the second order derivative of the exponential map that arises in traditional Lie group variational methods.  ...  The authors would also like to thank Geir Bogfjellmo and Håkon Marthinsen for sharing the code for their VRKMR method from [3] , which we used in the numerical comparisons with our method.  ... 
doi:10.3934/jcd.2022003 fatcat:7wwdphwt6faado2f7t4wxfggdu

Application of Bi-CGSTAB to waveguide discontinuity problems

Su Hua Wei, Ya Yan Lu
2002 IEEE Photonics Technology Letters  
Scattering at a waveguide end facet or other waveguide discontinuities can be calculated by an iterative method together with rational approximations to the related square root operators.  ...  Previous work uses the classical Neumann series as the iteration scheme.  ...  Since one iteration of N 1/2 or B 1/2 is 50% more expensive than an iteration in other methods, we compare the relative errors for the fourth iteration of N 1/2 , B 1/2 with the sixth iterations of the  ... 
doi:10.1109/68.998712 fatcat:o5vofuv4uvdennje44wscsvh34

High order methods for acoustic scattering: Coupling farfield expansions ABC with deferred-correction methods

Vianey Villamizar, Dane Grundvig, Otilio Rojas, Sebastian Acosta
2020 Wave motion  
As a result, high order numerical methods with an overall order of convergence equal to the order of the DC schemes are obtained.  ...  Arbitrary high order numerical methods for time-harmonic acoustic scattering problems originally defined on unbounded domains are constructed.  ...  Acknowledgments The first and third authors acknowledge the support provided by the European Union's Horizon  ... 
doi:10.1016/j.wavemoti.2020.102529 fatcat:vdokyv24gbhmtap43t32sbqufm

Higher order hybrid method of moments-physical optics modeling technique for radiation and scattering from large perfectly conducting surfaces

M. Djordjevic, B.M. Notaros
2005 IEEE Transactions on Antennas and Propagation  
An efficient and accurate higher order, large-domain hybrid computational technique based on the method of moments (MoM) and physical optics (PO) is proposed for analysis of large antennas and scatterers  ...  The PO part of the proposed technique, on the other hand, allows for a dramatic reduction in the computation time and memory with respect to the pure MoM higher order technique, which greatly extends the  ...  This mixed modeling approach optimizes the overall performance of the hybrid method in practical applications. Fig. 1 . 1 Decomposition of an electromagnetic structure into a MoM and a PO region.  ... 
doi:10.1109/tap.2004.841318 fatcat:crwvb3tskzfjhpfb7fsy7zq7ni

Model calculations in reconstructions of measured fields

Mihály Makai, Yuri Orechwa
2003 Open Physics  
The present work addresses an observed, and until now unexplained, convergence problem in the iterative solution in the application of the finite element method to boundary value problems.  ...  We use the appropriate and consistent orders of approximation on the boundary and within the volume so as to avoid non-convergence.  ...  Is an approximation available that provides an increasing order in every subspace? What is the impact of the applied approximations on the accuracy of the T matrix, which governs the iteration?  ... 
doi:10.2478/bf02475556 fatcat:zloycddq3zas5do7dn755y7mzi

The geometry of weighted low-rank approximations

J.H. Manton, R. Mahony, Yingbo Hua
2003 IEEE Transactions on Signal Processing  
The low-rank approximation problem is to approximate optimally, with respect to some norm, a matrix by one of the same dimension but smaller rank.  ...  It is known that under the Frobenius norm, the best low-rank approximation can be found by using the singular value decomposition (SVD).  ...  ACKNOWLEDGMENT The authors would like to thank P. Stoica for initial discussions on the weighted low-rank approximation problem and an anonymous reviewer for valuable comments.  ... 
doi:10.1109/tsp.2002.807002 fatcat:nid24x6wxrdj7lronwesio34xu

Elastic scatterer interaction via generalized Born series and far‐field approximations

P. J. Schafbuch, R. B. Thompson, F. J. Rizzo
1993 Journal of the Acoustical Society of America  
The resulting matrix equation may be solved in a fully implicit manner, but an implicit-iterative method is more efficient.  ...  The resulting matrix equation may be solved in a fully implicit manner, but an implicit-iterative method is more efficient.  ...  This reasoning continues for fifth, sixth, etc., orders and the sum takes the form of a power series of a complex variable.  ... 
doi:10.1121/1.405664 fatcat:ulwqqah2kbdpjpn6ajr6efnkde

A DOMAIN DECOMPOSITION METHOD BASED ON A GENERALIZED SCATTERING MATRIX FORMALISM AND A COMPLEX SOURCE EXPANSION

Enrica Martini, Giacomo Carli, Stefano Maci
2010 Progress in Electromagnetics Research B  
A general domain decomposition scheme based on the use of complex sources is presented for the electromagnetic analysis of complex antenna and/or scattering problems.  ...  Each obstacle is independently analyzed with the most appropriate technique and described through a generalized scattering matrix (GSM).  ...  sixth order (circles).  ... 
doi:10.2528/pierb10012110 fatcat:i7a7oopdrrbgdmv6ooy5b3ofqu

Very high-order Cartesian-grid finite difference method on arbitrary geometries [article]

Stéphane Clain, Diogo Lopes, Rui Pereira
2020 arXiv   pre-print
An arbitrary order finite difference method for curved boundary domains with Cartesian grid is proposed. The technique handles in a universal manner Dirichlet, Neumann or Robin condition.  ...  Numerical evidences based on the simple 2D convection-diffusion operators are presented to prove the ability of the method to reach at least the 6th-order with arbitrary smooth domains.  ...  Acknowledgements The authors acknowledge the financial support by FEDER -Fundo Europeu de Desenvolvimento Regional, through COMPETE 2020 -Programa Opera-  ... 
arXiv:2007.14680v1 fatcat:n4hiqoxh3vdszljvhfwwpbxrbi

Three-dimensional magnetotelluric inversion: data-space method

Weerachai Siripunvaraporn, Gary Egbert, Yongwimon Lenbury, Makoto Uyeshima
2005 Physics of the Earth and Planetary Interiors  
To reduce computational time, a relaxed convergence criterion is used for the iterative forward modeling code used to compute the sensitivity matrix.  ...  These difficulties are overcome with a data-space approach, where matrix dimensions depend on the size of the data set, rather than the number of model parameters.  ...  W.S. thanks the Faculty of Graduate Studies and Faculty of Science, Mahidol University for travel support to attend the XVI Induction Workshop in Santa Fe, USA, and also the Induction Workshop Committee  ... 
doi:10.1016/j.pepi.2004.08.023 fatcat:52jetamvazd2le6wxkd5lzcykq
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