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The singular value decomposition for polynomial systems

Robert M. Corless, Patrizia M. Gianni, Barry M. Trager, Stephen M. Watt
1995 Proceedings of the 1995 international symposium on Symbolic and algebraic computation - ISSAC '95  
This paper introduces singular value decomposition (SVD) algorithms for some standard polynomial computations, in the case where the coefficients are inexact or imperfectly known.  ...  Next, we adapt Lazard's u-resultant algorithm for the solution of overdetermined systems of polynomial equations to the inexact-coefficient case.  ...  roundoff perturbations) is the Singular Value Decomposition, or SVD.  ... 
doi:10.1145/220346.220371 dblp:conf/issac/CorlessGTW95 fatcat:je4opjy4lrdsxgpwh76ybnqtri

Perturbation by Decomposition: A New Approach to Singular Initial Value Problems with Mamadu-Njoseh Polynomials as Basis Functions

Mamadu E. J., Tsetimi J.
2020 Journal of Mathematics and System Science  
This paper focuses on the application of Mamadu-Njoseh polynomials (MNPs) as basis functions for the solution of singular initial value problems in the second-order ordinary differential equations in a  ...  Here, the proposed method is an hybrid of the perturbation theory and decomposition method.  ...  Let and * defines two separate solutions of Eq. (1), then | − * | = �� =0 − � =0 � Perturbation by Decomposition: A New Approach to Singular Initial Value Problems with Mamadu-Njoseh Polynomials as  ... 
doi:10.17265/2159-5291/2020.01.003 fatcat:izyfhzf24bggzmzd6qqm76hhtu

A DFT-based approximate eigenvalue and singular value decomposition of polynomial matrices

Mahdi Tohidian, Hamidreza Amindavar, Ali M. Reza
2013 EURASIP Journal on Advances in Signal Processing  
In this article, we address the problem of singular value decomposition of polynomial matrices and eigenvalue decomposition of para-Hermitian matrices.  ...  This formulation of polynomial matrix decomposition allows for controlling spectral properties of the decomposition.  ...  Introduction Polynomial matrices have been used for a long time for modeling and realization of multiple-input multipleoutput (MIMO) systems in the context of control theory [1] .  ... 
doi:10.1186/1687-6180-2013-93 fatcat:w3g3lrf2g5hk3aad4dr27qkdze

On the evaluation of a matrix polynomial

S.C.D. Roy, S. Minocha
1992 IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications  
Also, the value of N max determines the number of optimal decompositions available for substitution.  ...  The criterion is sufficient for BIBO stability and also necessary for systems without singularities of the second kind.  ... 
doi:10.1109/81.257297 fatcat:l5y6g3eafff6ph2vivi4adt5ji

The polar decomposition of block companion matrices

G. Kalogeropoulos, P. Psarrakos
2005 Computers and Mathematics with Applications  
|If the mimmum or the maximum singular value of CL is equal to 1, then the polar decomposition of CL is equivalent to the polar decomposition of the matrix Ao.  ...  Hence, we conclude that our results add one more possibility for testing numerical algorithms relative to polar decomposition and singular value decomposition. solution xo is known as an ezgenveetor of  ... 
doi:10.1016/j.camwa.2005.02.014 fatcat:xhapphp7eje5xad2mlt2knemg4

Singular Value Decomposition of the Radial Distribution Function for Hard Sphere and Square Well Potentials

Travis Hoppe, Dennis Salahub
2013 PLoS ONE  
We compute the singular value decomposition of the radial distribution function g(r) for hard sphere, and square well solutions.  ...  In addition, we find that the coefficient vectors describing the magnitude of each basis vector are well described by a low-order polynomial.  ...  The singular values for the SW system, shown in Figure 1 , indicate a sharp decomposition by w and E. The spectrum of Figure 1 . Rank sorted normalized singular value spectrum.  ... 
doi:10.1371/journal.pone.0075792 pmid:24143174 pmcid:PMC3797047 fatcat:jrwkph3wmzhxxg5b53hyeqneue

Predicting Directed Links Using Nondiagonal Matrix Decompositions

Jerome Kunegis, Jorg Fliege
2012 2012 IEEE 12th International Conference on Data Mining  
We show that our method can be used to compute better lowrank approximations to a polynomial of a network's adjacency matrix than using the singular value decomposition, and that a higher precision can  ...  We present a method for trust prediction based on nondiagonal decompositions of the asymmetric adjacency matrix of a directed network.  ...  The same learning method as for the eigenvalue decomposition can be used with the singular value decomposition of the asymmetric matrix A.  ... 
doi:10.1109/icdm.2012.16 dblp:conf/icdm/KunegisF12 fatcat:a7ypf7c27rfjrhc622n42fnnpm

Identification of FIR Wiener systems with unknown, non-invertible, polynomial non-linearities

Seth L. Lacy, Dennis S. Bernstein
2003 International Journal of Control  
We then consider four methods for extracting the coefficients of the non-linearity and impulse response: direct algebraic solution, singular value decomposition, multi-dimensional singular value decomposition  ...  In this paper we study the identification of single-input single-output Wiener systems with finite impulse response dynamics and polynomial output non-linearities.  ...  The multi-dimensional singular value decomposition approach produced estimates comparable to the first singular value decomposition approach, but the multidimensional singular value decomposition is more  ... 
doi:10.1080/00207170310001599122 fatcat:i7ydkgxwhne2xg5hztbrrfcqv4

Identification of FIR Wiener systems with unknown, noninvertible, polynomial nonlinearities

S.L. Lacy, D.S. Bernstein
2002 Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301)  
We then consider four methods for extracting the coefficients of the non-linearity and impulse response: direct algebraic solution, singular value decomposition, multi-dimensional singular value decomposition  ...  In this paper we study the identification of single-input single-output Wiener systems with finite impulse response dynamics and polynomial output non-linearities.  ...  The multi-dimensional singular value decomposition approach produced estimates comparable to the first singular value decomposition approach, but the multidimensional singular value decomposition is more  ... 
doi:10.1109/acc.2002.1023129 fatcat:tr6eawd66nggrjdmhkc4my5aeu

Wavefront correction of optical beam for large space mirrors using robust control techniques

Jae Jun Kim, Daniel C. Burtz, Brij N. Agrawal
2011 Acta Astronautica  
An H 1 robust control technique is considered for the control of the adaptive optics system with the reduced number of inputs and outputs using singular value decomposition and Zernike polynomials.  ...  Because of the weight and launch constraints for spacebased optics systems, the mirrors will have to be segmented and light-weight, resulting in increased flexibility and lower structural frequencies.  ...  There are two different bases for model reduction used in this paper: singular value decomposition and Zernike polynomials.  ... 
doi:10.1016/j.actaastro.2010.07.017 fatcat:qzhwq72wubaenpoc6jkynb67lq

A study of the effect of uncertainties when calculating the singular value decomposition of a polynomial matrix

J.A. Foster, J.G. McWhirter, M.R. Davies, J.A. Chambers
2010 2010 IEEE International Conference on Acoustics, Speech and Signal Processing  
An algorithm has been recently proposed by the authors for calculating a polynomial matrix singular value decomposition (SVD) based upon polynomial matrix QR decomposition.  ...  In particular, the performance of the two methods is examined when each is used as part of a broadband multiple-input multiple-output (MIMO) communication system by means of average bit error rate simulations  ...  THE SINGULAR VALUE DECOMPOSITION OF A POLYNOMIAL MATRIX The SVD of a polynomial matrix A(z) ∈ C p×q can be expressed as U(z)A(z) V(z) = Λ(z) (3) where U(z) ∈ C p×p and V(z) ∈ C q×q are both paraunitary  ... 
doi:10.1109/icassp.2010.5495728 dblp:conf/icassp/FosterMDC10 fatcat:oaxoafsr2jho7bpc47qojenaf4

Singular value decomposition and its application to numerical inversion for ray transforms in 2D vector tomography

Evgeny Y. Derevtsov, Anton V. Efimov, Alfred K. Louis, Thomas Schuster
2011 Journal of Inverse and Ill-Posed Problems  
Based on the obtained decompositions inversion formulas are derived and the polynomial approximations for the inverse operators are obtained.  ...  The goal is to construct SVD-decompositions of the operators and invert them approximately by means of truncated decomposition for the parallel scheme of data acquisition.  ...  Finally the polynomial approximation is constructed using the truncated singular values decomposition (2.12).  ... 
doi:10.1515/jiip.2011.047 fatcat:lcr2odnlezdkpc2xyjx4rqeqhq

On Computing a Cell Decomposition of a Real Surface Containing Infinitely Many Singularities [chapter]

Daniel J. Bates, Daniel A. Brake, Jonathan D. Hauenstein, Andrew J. Sommese, Charles W. Wampler
2014 Lecture Notes in Computer Science  
The previously existing algorithm for surfaces is restricted to the "almost smooth" case, i.e., the given surface must contain only finitely many singular points.  ...  These algorithms use homotopy continuation to produce a cell decomposition.  ...  Introduction Polynomial systems appear throughout the sciences, engineering, and mathematics.  ... 
doi:10.1007/978-3-662-44199-2_39 fatcat:zytfrroej5gdvitwztxe4oxg6a

Exact and approximate polynomial decomposition methods for signal processing applications

Sefa Demirtas, Guolong Su, Alan V. Oppenheim
2013 2013 IEEE International Conference on Acoustics, Speech and Signal Processing  
In this paper, we summarize the fundamentals of functional composition and decomposition for polynomials from the perspective of exploiting them in signal processing.  ...  We compare exact polynomial decomposition algorithms for sequences that are exactly decomposable when expressed as a polynomial, and approximate decomposition algorithms for those that are not exactly  ...  signal processing, including singular value decomposition of matrices and implementation of LTI systems as a cascade of at most second order systems among many others.  ... 
doi:10.1109/icassp.2013.6638689 dblp:conf/icassp/DemirtasSO13 fatcat:c63loi7nzrdrbarp7wt7wtzmm4

Singular value decomposition of fractional integration operators in L2-spaces with weights

R. GORENFLO, VU KIM TUAN
1995 Journal of Inverse and Ill-Posed Problems  
For the fractional integration operators of any positive order on the half-line and on a bounded interval we explicitly present a singular value decomposition, thereby considering these operators as acting  ...  The results obtained amount to an interpretation of properties of systems of orthogonal polynomials.  ...  In this paper the singular value decompositions of the operator I α a for some special weighted L 2 -spaces are obtained, and it is interesting to notice that for some cases the singular values decay like  ... 
doi:10.1515/jiip.1995.3.1.1 fatcat:pvt3x6l47fdkdfbyo2wjvos3gm
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