solving systems of linear and quadratic equations calculator

... Iteration Berzig and Samet Fixed Point Theory and Applications 2011, 2011:89 http://www.fixedpointtheoryandapplications.com/content/2011/1/89 Page of 10 3.2 System of three nonlinear matrix equations ... doi:10.1137/05062873 Shi, X, Liu, F, Umoh, H, Gibson, F: Two kinds of nonlinear matrix equations and their corresponding matrix sequences Linear Multilinear Algebra 52, 1–15 (2004) doi:10.1080/0308108031000112606 ... Fixed Point Theory and Applications 2011, 2011:89 http://www.fixedpointtheoryandapplications.com/content/2011/1/89 Page of 10 where q3 = 1/6 Proof Follows from Propositions 3.3, 3.4 and Theorem 2.1...

Ngày tải lên: 20/06/2014, 22:20

... analogy between the properties of linear inequalities and those of systems of linear equations (everything connected with linear equations has been studied for a long time and in much detail) Until ... easily extended to systems in a larger number of unknowns The solution of any system of linear inequalities is in the long run reduced to the solution of a number of systems of linear equations We ... of this small book to acquaint the reader with the various aspects of the theory of systems of linear inequalities, viz with the geometrical aspect of the matter and some of the methods for solving...

Ngày tải lên: 08/04/2014, 10:42

... solutions and error estimates for linear systems of difference and differential equations, ” Journal of Mathematical Analysis and Applications, vol 290, no 1, pp 343– 362, 2004 11 S Bodine and D A ... equivalence of perturbed linear systems of differential and difference equations, ” Journal of Mathematical Analysis and Applications, vol 326, no 2, pp 1174–1189, 2007 12 R D Driver, G Ladas, and P N ... A D Applelby, I Gy˝ ri, and D W Reynolds, “On exact convergence rates for solutions of linear o systems of Volterra difference equations, ” Journal of Difference Equations and Applications, vol 12,...

Ngày tải lên: 22/06/2014, 11:20

... which is impossible The proof of next result is similar to the proof of [2, Proposition 3.3] and it will be omitted This proof makes essential use of the nonexistence of prime period-two solution ... competitive and cooperative difference equations, Journal of Difference Equations and Applications (1998), no 5-6, 335–357 M R S Kulenovi´ : Department of Mathematics, University of Rhode Island, Kingston, ... y-axis and the portion of W s in Q1 (E) is unbounded We now state the major result of this section The proof of this result is similar to the proof of [2, Theorem 3.1] and will be omitted Theorem...

Ngày tải lên: 22/06/2014, 22:20

... for a linear system of differential equations with rational coefficients The goal of this paper is to develop a general theory of “isomonodromy” transformations for linear systems of difference equations ... The matrix elements of S and T are rational functions of the matrix elements of X and Y which not depend on the spectra of X and Y Proof Lemma 3.3 proves the uniqueness and shows how to construct ... note, first of all, that it suffices to provide a proof if one of the κi ’s is equal to ±1 and one of the δj ’s is equal to ∓1 with all other κ’s and δ’s equal to zero The proof will consist of several...

Ngày tải lên: 14/02/2014, 17:20

Ngày tải lên: 14/03/2014, 13:20

... the use of Gronwall inequality Then, v ≤ u in DT , and the proof of part i of the lemma is completed The similar argument gives the proof of part ii of the lemma Advances in Difference Equations ... where α2 and α3 depend only on d and the parameters M, a0 , θ0 , α0 , μ1 , μ2 , ν M , μ M , and independent of m 0, Proof By Hypothesis H , 3.20 , and 3.27 , the proof similar to that of 15, Lemma ... fund of Department of Education of Sichuan Province 10ZC127 and the research fund of Sichuan College of Education CJYKT09-024 References C V Pao, Nonlinear Parabolic and Elliptic Equations, Plenum...

Ngày tải lên: 21/06/2014, 05:20

... suggested to the study of stability and estimates of solutions of 1.1 Exponential Stability and Estimates of the Convergence of Solutions to Stable Systems First we give two definitions of stability to ... H , ϕ1 G1 , H and ϕ2 G2 , H , have the same meaning as in Part The proof of the following theorem is similar to the proofs of Theorems 2.5 and 2.6 and its statement in the case of p exactly coincides ... Stability of Dynamical Systems Under Random Perturbations of Parameters Algebraic ı Criteria, Naukova Dumka, Kiev, Ukraine, 1989 D Ya Khusainov and E A Yunkova, “Investigation of the stability of linear...

Ngày tải lên: 21/06/2014, 11:20

... Description of the problem considered The motivation of our investigation goes back to [10] dealing with the linear system of differential equations with constant coefficients and constant delay One of the ... Discrete systems of the form (1.1) containing only one delay are often called systems with pure delay The main goal of the present paper is to extend the notion of the delayed exponential of a matrix ... accordance with the theory of linear equations, as the sum of the solution of adjoint homogeneous problem (3.1), (3.2) (satisfying the same initial data) and a particular solution of (3.15) being zero...

Ngày tải lên: 22/06/2014, 22:20

... number of initial conditions should be equal to the number of roots of the characteristic polynomial inside the unit circle and, of course, the number of conditions at the end of the interval of ... if the number of initial conditions is equal to the number of roots of the characteristic polynomial inside the unit circle and the number of conditions at the end of the interval of integration ... k −2 This completes the proof Lemma 3.5 The solutions ρk (z) and σk (z) of (3.4) are linearly independent (3.14) 10 Difference equations and the stability problem Proof Let us consider the Casorati...

Ngày tải lên: 23/06/2014, 00:20

... notion of the central exponent and some properties of central exponents of linear DAEs of index In Sec we investigate exponential asymptotic stability of linear DAEs with respect to small linear ... derive some properties of the central exponent of linear DAE of index and of its corresponding ODE Theorem 2.2 Suppose that (2.1) is a linear DAE of index and the matrices A(t), B(t), A−1 , P (t) are ... a C-function of im P (t) of (3.11) Thus, C-classes R of (2.1) and RUimP of the invariant subspace im P of the solution space of (3.11) coincide Suppose that xδ (t) is a solution of the perturbed...

Ngày tải lên: 06/08/2014, 05:20

... Cataloging-in-Publication Data [Analyse des systèmes linéaires/Commande des systèmes linéaires eng] Analysis and control of linear systems analysis and control of linear systems/ edited by Philippe de Larminat p cm ... BOUCHER and Patrick TURELLE 43 2.1 Reminders on the systems 2.1.1 Internal representation of determinist systems: the concept of state 2.1.2 Equations of state and equations ... equations of measurement for continuous systems 2.1.3 Case of linear systems 2.1.4 Case of continuous and invariant linear systems ...

Ngày tải lên: 09/08/2014, 06:23

... at 5%) and ω t m according to the damping ξ Figure 1.21 ω0 tr and ω0 tm according to the damping ξ 30 Analysis and Control of Linear Systems The alternation of slow and fast variations of product ... final value of the response at the end of time T, which is called time constant of the system The response reaches 0.63 K in T and 0.95 K in T 24 Analysis and Control of Linear Systems Figure ... jf0 20 Analysis and Control of Linear Systems Table 1.1 sums up the features of a system’s transfer function, the existence conditions of its frequency response and the possibility of performing...

Ngày tải lên: 09/08/2014, 06:23

... Analysis and Control of Linear Systems 3.2.2 Delay and lead operators The concept of an operator is interesting because it enables a compact formulation of the description of signals and systems ... development of X (z) by polynomial division according to 86 Analysis and Control of Linear Systems the decreasing powers of z −1 or apply the method of deviations, starting from the definition of the ... z-transform of this impulse response 102 Analysis and Control of Linear Systems Due to this relation and Table 3.5, we will be able to easily obtain the transfer function of the discretized system and, ...

Ngày tải lên: 09/08/2014, 06:23

... 110 Analysis and Control of Linear Systems The object of this chapter is to describe certain structural properties of linear systems that condition the resolution of numerous control problems ... solutions, the use of rollouts and in particular the fixed poles and the remaining degrees of freedom, we can mention [MAL 93, MAL 97] and [MAR 94, MAR 99] Structural Properties of Linear Systems 137 ... conclusions and lists the main references 4.1.1 Vector spaces, linear applications Let X and Y be real vector spaces of finite dimension and V ⊂ X and W ⊂ Y, two sub-spaces Let L: X → Y be a linear...

Ngày tải lên: 09/08/2014, 06:23

... proximity of ν0 152 Analysis and Control of Linear Systems Figure 5.1 Typical power spectrum of an MA (left) or AR (right) model In the case of a single denominator (nc = 0), we talk of an AR ... 144 Analysis and Control of Linear Systems On the other hand, the Fourier transform preserves the energy (Parseval theorem) Indeed, the energy of a continuous-time signal y(t) or of a discrete-time ... my )) ∀κ ∈ Z [5.18] 146 Analysis and Control of Linear Systems are independent of index k, i.e independent of the time origin σy = ryy [0] is the r [κ] variance of the signal considered yy2 is...

Ngày tải lên: 09/08/2014, 06:23

... Analysis and Control of Linear Systems u (t ) = − K x(t ) + e(t ) [6.2] where K is an m × n matrix (Figure 6.1) and signal e(t ) represents the input of the looped system The equations of the looped ... result cannot be extended to the 162 Analysis and Control of Linear Systems case of multi-control systems As indicated in Chapter 2, the equations of state can be expressed in companion form: ... control, whereas the increase of ξ leads to better dynamics 164 Analysis and Control of Linear Systems Figure 6.2 Stabilization by pole placement 6.3 Reconstruction of state and observers 6.3.1 General...

Ngày tải lên: 09/08/2014, 06:23

... 196 Analysis and Control of Linear Systems in performing the roles of the procedure, in connection with a structure and behavior of components They are used for the design of procedure monitoring, ... described in the form of non -linear differential equations in the dynamic case and/ or in the form of algebraic equations in the static case These equations describe the main laws of the physical world, ... one hand, the problem of identification (and also the problem of simulation and control) is made much easier by the computing tool and is already well known in data analysis (linear or non-linear...

Ngày tải lên: 09/08/2014, 06:23

... 228 Analysis and Control of Linear Systems 8.1.1 About linear equations The specific techniques of linear differential equations are fundamentally exact integration ... requirements of speed and accuracy accessible in simulation 8.2 Standard linear equations 8.2.1 Definition of the problem We will adopt the notations usually used to describe the state forms and linear ... observations Through an extension of the notations introduced at the 236 Analysis and Control of Linear Systems beginning of this chapter, we will deal with equations of the form: ◦ x (t) = f (x,...

Ngày tải lên: 09/08/2014, 06:23