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Page 1271 of Mathematical Reviews Vol. , Issue 2003B [page]

2003 Mathematical Reviews  
In this paper we present an ap- proach, based upon the ABS methods, to solve a general system of linear Diophantine equations.  ...  , Emilio (I-BERG-MS; Bergamo) A class of ABS algorithms for Diophantine linear systems.  ... 

ABS methods for continuous and integer linear equations and optimization

Spedicato Emilio, Bodon Elena, Xia Zunquan, Mahdavi-Amiri Nezam
2009 Central European Journal of Operations Research  
The ABS method are based on the rank reducing matrix update due to Egerváry and can be considered as the most fruitful extension of such technique.  ...  The work on ABS methods began almost thirty years.  ...  Keywords Egerváry rank reduction matrix update · ABS methods · Linear systems · Diophantine Linear systems · Quasi-Newton equation · Feasible direction methods for linearly constrained optimization · Simplex  ... 
doi:10.1007/s10100-009-0128-9 fatcat:6b5f6yakwfd47pjovypmt2ruzu

Title index to volumes 23–28, 1979

1979 Linear Algebra and its Applications  
Programming, 25:151 Univalence and P-Matrices, On, 24239 Unsymmetric Positive Definite Linear Systems, 2885 Variations on the Cauchy-Schwartz lnequality. 27:81 AB)+ =B,;AI;, 25:107 Extension of the Dulmage-Mendelsohn  ...  Generalized Inversion, On the, 27:141 Maximal Multiplicative Complexity of a Family of Bilinear Forms, On the, 27:l Maximum Problem for Matrices, A, 28:193 Methods for Solving the Matrix Equation I'B  ... 
doi:10.1016/0024-3795(79)90142-3 fatcat:fxuk6jzpmzcnhexcufvueraoym

ABS algorithms for linear equations and optimization

Emilio Spedicato, Zunquan Xia, Liwei Zhang
2000 Journal of Computational and Applied Mathematics  
In this paper we review basic properties and the main achievements obtained by the class of ABS methods, developed since 1981 to solve linear and nonlinear algebraic equations and optimization problems  ...  Acknowledgements Work performed in the framework of a research supported partially by MURST Programma Coÿnanziato 1997.  ...  Once p is determined, one can determine z in two ways, namely, (B1) Solve by any ABS method the overdetermined compatible system C T z = g − Gp (23) by removing at step (B) of the ABS algorithm the (n  ... 
doi:10.1016/s0377-0427(00)00419-2 fatcat:zdlmqixaqnetxpxfk6bw4k3v6m

Page 593 of Mathematical Reviews Vol. , Issue 89A [page]

1989 Mathematical Reviews  
In each case the method involves one spectral factoriza- tion and the solution of one Diophantine equation.  ...  Frequency domain and state space methods for linear systems (Stockholm, 1985), 271-284, North-Holland, Amsterdam-New York, 1986.  ... 

General solution of full row rank linear systems of equations using a new compression ABS model

Leila Asadbeigi, Mahmoud Paripour, Esmaeil Babolian, Shahnam Javadi
2017 Mathematical Sciences  
This paper describes two new ABS algorithms based on two-step ABS methods for solving general solution of full row rank linear systems of equations.  ...  The number of multiplications for these new schemes is half of the storage needed by the Gaussian elimination method.  ...  ABS methods were introduced by Abaffy, Broyden, and Spedicato initially for solving a determined or underdetermined linear system and later extended for linear least squares, nonlinear equations, optimization  ... 
doi:10.1007/s40096-017-0236-y fatcat:xud4rmfppjhezg5zyst5v7aj6i

On the Destruction of Resonant Lagrangean Tori in Hamiltonian Systems [chapter]

Henk W. Broer, Heinz Hanßmann, Jiangong You
2013 Recent Trends in Dynamical Systems  
Starting from Poincaré's fundamental problem of dynamics, we consider perturbations of integrable Hamiltonian systems in the neighbourhood of resonant Lagrangean (i.e. maximal) invariant tori with a single  ...  For a better understanding of the dynamics, both qualitatively and quantitatively, we also investigate the singular tori and the way in which they are being unfolded by the action variables.  ...  Acknowledgements We thank an anonymous referee for challenging us with the example H(ϕ, I) = H 0 (I) + εH 1 (ϕ) of a non-versal perturbation.  ... 
doi:10.1007/978-3-0348-0451-6_13 fatcat:atwfyvillbc6darjm3hwllbbxi

On Using Linear Diophantine Equations for in-Parallel Hiding of Decision Tree Rules

Georgios Feretzakis, Dimitris Kalles, Vassilios S. Verykios
2019 Entropy  
We propose a look ahead technique using linear Diophantine equations to add the appropriate number of instances while maintaining the initial entropy of the nodes.  ...  This method can be used to hide one or more decision tree rules optimally.  ...  This implementation demonstrates the use of Diophantine equations on our technique and consists of only one part of our proposed method.  ... 
doi:10.3390/e21010066 pmid:33266782 fatcat:6ilsbsrlcjcqlfzdvtb2vzw4ye

Robust flight control systems - A parameter space design

ALBERTO CAVALLO, GIUSEPPE DE MARIA, LEOPOLDO VERDE
1992 Journal of Guidance Control and Dynamics  
If a,,, # 0, a(s) and b(s) are coprime, and v = vw — 1, where » is the observability index of a state re- alization of b(s)/a(s), then rankS =n+v+1 (16) o Theorem 1 allows us to solve the generalized diophantine  ...  If a'(s) = vi_,(s)a@’ + s” b'(s) = v7_,(s)B' are coprime polynomials, then rank (B’ AB’ - - - AB’) = Wy=v,-1 (A9) Where », is the reachability index of the pair (A’, B’) and 07 | | —d’ (A10) 1, | denotes  ... 
doi:10.2514/3.20970 fatcat:sdizx7xlofd6fhunlfnwgrcqge

Nekhoroshev's estimates for quasi-periodic time-dependent perturbations [article]

Abed Bounemoura
2015 arXiv   pre-print
In this paper, we consider a Diophantine quasi-periodic time-dependent analytic perturbation of a convex integrable Hamiltonian system, and we prove a result of stability of the action variables for an  ...  This extends known results for periodic time-dependent perturbations, and partly solves a long standing conjecture of Chirikov and Lochak.  ...  The Lochak method crucially relies on the existence of periodic orbits for the integrable system, that is on the existence of periodic frequencies.  ... 
arXiv:1506.06470v1 fatcat:lljgy5ofibc3ri634bv3nfnjmu

Nekhoroshev's estimates for quasi-periodic time-dependent perturbations

Abed Bounemoura
2016 Commentarii Mathematici Helvetici  
In this paper, we consider a Diophantine quasi-periodic time-dependent analytic perturbation of a convex integrable Hamiltonian system, and we prove a result of stability of the action variables for an  ...  This extends known results for periodic time-dependent perturbations, and partly solves a long standing conjecture of Chirikov and Lochak.  ...  The Lochak method crucially relies on the existence of periodic orbits for the integrable system, that is on the existence of periodic frequencies.  ... 
doi:10.4171/cmh/399 fatcat:uxuoz74x3zc6nlrstsuwc4ihni

A method for the study of whiskered quasi-periodic and almost-periodic solutions in finite and infinite dimensional Hamiltonian systems

Yannick Sire, Rafael Llave, Ernest Fontich
2009 Electronic Research Announcements in Mathematical Sciences  
The method applies to finite dimensional systems and also to lattice systems and to PDE's including some ill posed ones.  ...  We describe a method to study the existence of whiskered quasiperiodic solutions in Hamiltonian systems.  ...  On the other hand, |∂ k F i ||∂ j F k | is a bound on the effect of the system j on the system i interacting through the system k.  ... 
doi:10.3934/era.2009.16.9 fatcat:bth5t2xqdbe6rlmovnpkyyqb3q

Causal IIR Audio Precompensator Filters Subject to Quadratic Constraints

Simon Widmark
2018 IEEE/ACM Transactions on Audio Speech and Language Processing  
compensated system.  ...  A method for designing causal filters subject to constraints on the power gains in a large number of small frequency intervals is also proposed.  ...  Formulating the Diophantine equation by a system of linear equations, this matrix here attains a dimension of 21682|21682 elements.  ... 
doi:10.1109/taslp.2018.2839355 fatcat:65677j2rdjhb7b4vz62rz2s3vu

A Diophantine duality applied to the KAM and Nekhoroshev theorems [article]

Abed Bounemoura
2012 arXiv   pre-print
In this paper, we use geometry of numbers to relate two dual Diophantine problems. This allows us to focus on simultaneous approximations rather than small linear forms.  ...  We obtain two results of stability, in the spirit of the KAM and Nekhoroshev theorems, in the model case of a perturbation of a constant vector field on the n-dimensional torus.  ...  This statement is analogous to the Nekhoroshev theorem for perturbation of linear integrable Hamiltonian systems.  ... 
arXiv:1204.1608v2 fatcat:lk2etbiv7nfrbekadxp2mmgvc4

A Diophantine duality applied to the KAM and Nekhoroshev theorems

Abed Bounemoura, Stéphane Fischler
2013 Mathematische Zeitschrift  
In this paper, we use geometry of numbers to relate two dual Diophantine problems. This allows us to focus on simultaneous approximations rather than small linear forms.  ...  We obtain two results of stability, in the spirit of the KAM and Nekhoroshev theorems, in the model case of a perturbation of a constant vector field on the n-dimensional torus.  ...  This statement is analogous to the Nekhoroshev theorem for perturbation of linear integrable Hamiltonian systems.  ... 
doi:10.1007/s00209-013-1174-5 fatcat:cpddjsql45h43ecjmfkvlp7qou
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