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The singular value decomposition for polynomial systems
1995
Proceedings of the 1995 international symposium on Symbolic and algebraic computation - ISSAC '95
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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
2020
Journal of Mathematics and System Science
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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
2013
EURASIP Journal on Advances in Signal Processing
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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
1992
IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications
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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
2005
Computers and Mathematics with Applications
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|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
2013
PLoS ONE
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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
2012
2012 IEEE 12th International Conference on Data Mining
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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
2003
International Journal of Control
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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
2002
Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301)
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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
2011
Acta Astronautica
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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
2010
2010 IEEE International Conference on Acoustics, Speech and Signal Processing
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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
2011
Journal of Inverse and Ill-Posed Problems
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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]
2014
Lecture Notes in Computer Science
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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
2013
2013 IEEE International Conference on Acoustics, Speech and Signal Processing
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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
1995
Journal of Inverse and Ill-Posed Problems
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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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