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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
*

This paper introduces

doi:10.1145/220346.220371
dblp:conf/issac/CorlessGTW95
fatcat:je4opjy4lrdsxgpwh76ybnqtri
*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. ...##
###
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
*

This paper focuses on

doi:10.17265/2159-5291/2020.01.003
fatcat:izyfhzf24bggzmzd6qqm76hhtu
*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 ...##
###
A DFT-based approximate eigenvalue and singular value decomposition of polynomial matrices

2013
*
EURASIP Journal on Advances in Signal Processing
*

In this article, we address

doi:10.1186/1687-6180-2013-93
fatcat:w3g3lrf2g5hk3aad4dr27qkdze
*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] . ...##
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On the evaluation of a matrix polynomial

1992
*
IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications
*

Also,

doi:10.1109/81.257297
fatcat:l5y6g3eafff6ph2vivi4adt5ji
*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. ...##
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The polar decomposition of block companion matrices

2005
*
Computers and Mathematics with Applications
*

|If

doi:10.1016/j.camwa.2005.02.014
fatcat:xhapphp7eje5xad2mlt2knemg4
*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 ...##
###
Singular Value Decomposition of the Radial Distribution Function for Hard Sphere and Square Well Potentials

2013
*
PLoS ONE
*

We compute

doi:10.1371/journal.pone.0075792
pmid:24143174
pmcid:PMC3797047
fatcat:jrwkph3wmzhxxg5b53hyeqneue
*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. ...##
###
Predicting Directed Links Using Nondiagonal Matrix Decompositions

2012
*
2012 IEEE 12th International Conference on Data Mining
*

We show that our method can be used to compute better lowrank approximations to a

doi:10.1109/icdm.2012.16
dblp:conf/icdm/KunegisF12
fatcat:a7ypf7c27rfjrhc622n42fnnpm
*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. ...##
###
Identification of FIR Wiener systems with unknown, non-invertible, polynomial non-linearities

2003
*
International Journal of Control
*

We then consider four methods

doi:10.1080/00207170310001599122
fatcat:i7ydkgxwhne2xg5hztbrrfcqv4
*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 ...##
###
Identification of FIR Wiener systems with unknown, noninvertible, polynomial nonlinearities

2002
*
Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301)
*

We then consider four methods

doi:10.1109/acc.2002.1023129
fatcat:tr6eawd66nggrjdmhkc4my5aeu
*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 ...##
###
Wavefront correction of optical beam for large space mirrors using robust control techniques

2011
*
Acta Astronautica
*

An H 1 robust control technique is considered

doi:10.1016/j.actaastro.2010.07.017
fatcat:qzhwq72wubaenpoc6jkynb67lq
*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*. ...##
###
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
*

An algorithm has been recently proposed by

doi:10.1109/icassp.2010.5495728
dblp:conf/icassp/FosterMDC10
fatcat:oaxoafsr2jho7bpc47qojenaf4
*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 ...##
###
Singular value decomposition and its application to numerical inversion for ray transforms in 2D vector tomography

2011
*
Journal of Inverse and Ill-Posed Problems
*

Based on

doi:10.1515/jiip.2011.047
fatcat:lcr2odnlezdkpc2xyjx4rqeqhq
*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). ...##
###
On Computing a Cell Decomposition of a Real Surface Containing Infinitely Many Singularities
[chapter]

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. ...

##
###
Exact and approximate polynomial decomposition methods for signal processing applications

2013
*
2013 IEEE International Conference on Acoustics, Speech and Signal Processing
*

In this paper, we summarize

doi:10.1109/icassp.2013.6638689
dblp:conf/icassp/DemirtasSO13
fatcat:c63loi7nzrdrbarp7wt7wtzmm4
*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. ...##
###
Singular value decomposition of fractional integration operators in L2-spaces with weights

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 ...

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