linear systems of equations matrices calculator

... equal to I. The proof of uniqueness is complete. To prove the existence we note, first of all, that it suffices to provide a proof if one of the κ i ’s is equal to ±1 and one of the δ j ’s is equal ... solutions of isomonodromy problems for such systems of difference equations. In the case of one-interval gap probability this has been done (in a different language) in [Bor], [BB]. One example of the ... ALEXEI BORODIN Most of the results of the present paper can be carried over to the case of q-difference equations of the form Y (qz)=A(z)Y (z). The q-difference Schlesinger equations are, cf. (3)–(6), (3q) (4q) (5q) (6q) B i (...

Ngày tải lên: 14/02/2014, 17:20

... figure is reduced for the visualization. Enclosing solutions of systems of equations involving ODE Aurelien Lejeune National Institute of Informatics 2-1-2 Hitotsubashi, Chyoda-ku Tokyo 101-8430 ... part. Mots-clefs : syst`emes hybrides, equations differentielles ordinaires, anal- yse par intervalles. References 1. Hansen, E. and Sengupta, S.: Bounding solutions of systems of equations using interval ... Solving of Hybrid Constraint Systems. 3rd IFAC Conference on Analysis and Design of Hybrid Systems (ADHS09) (to appear) 10. Kăuhn, W.: Rigorously Computed Orbits of Dynamical Systems Without the Wrap- ping...

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... solutions of a system of linear equations. Throughout this paper, R will denote the set of real numbers, C the set of complex numbers, and M n the complex vector space of complex n ì n matrices. A function ... λ  v 3 18 which approaches to ∞ as k →∞. T his completes the proof. We now consider applications of preceding theorems to approximation of solution of a linear system Ax  b, where A ∈ M n and b a given vector ... index of the eigenvalue 0 of Q −1 A is the index of eigenvalue 1 of B  I − Q −1 A.ThusbyLemma 5, C n  Q −1 RA ⊕ NA. For every vector v ∈ C n ,letv r and v n denote the component of v...

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... inequalities is in the long run reduced to the solution of a number of systems of linear equations. We shall regard the solution of a system of linear equations as something simple, as an elementary operation, and shall not be I ... of a System in Three Unknowns 44 7 Systems of Linear Inequalities in Any Number of Unknowns 52 8. The Solution of a System of Linear Inequalities 'by Successive Reduction of the Number of Unknowns 57 9. Incompatible Systems ... Visualization of Systems of Linear Inequalities In Two or Three " . Unknowns 17 I - 3. The Convex Hull of a System of Points 22 4. A Convex Polyhedral Cone 25 5. The Feasible Region of a System of Linear Inequalities...

Ngày tải lên: 08/04/2014, 10:42

... solving different classes of systems of nonlinear matrix equations involving Lipshitzian mappings. 2000 Mathematics Subject Classifications: 15A24; 65H05. Keywords: nonlinear matrix equations, Lipshitzian ... classes of nonlinear matrix equations (see [8-21]). In this study, we consider the following problem: Find (X 1 , X 2 , ,X m ) ẻ (P(n)) m solution to the following system of nonlinear matrix equations: X r i i = ... for the study of solutions to systems of nonlinear matrix equations involving contractive mappings. We first review the Thompson metric on the open convex cone P(n)(n ≥ 2), the set of all nìn Hermitian...

Ngày tải lên: 20/06/2014, 22:20

... Constant-sign solutions of a system of Fredholm integral equations. Acta Appl Math. 80,57–94 (2004) 7. Agarwal, RP, O’Regan, D, Wong, PJY: Eigenvalues of a system of Fredholm integral equations. Math ... Triple solutions of constant sign for a system of Fredholm integral equations. Cubo. 6,1–45 (2004) 9. Agarwal, RP, O’Regan, D, Wong, PJY: Constant-sign solutions of a system of integral equations: ... this article as: Agarwal et al.: Existence results of Brezis-Browder type for systems of Fredholm integral equations. Advances in Difference Equations 2011 2011:43. Submit your manuscript to a...

Ngày tải lên: 20/06/2014, 22:20

... or tends to zero as t đ . Proof. The proof of the corollary is similar to the proof of Corollary 3.3 and so it is omitted. From the above results on the oscillation of odd-order differential equation ... Oscillation of solutions to odd-order nonlinear neutral functional differential equations. Electron J Diff Equ. 23,1–12 (2011) 15. Rath, RN, Padhy, LN, Misra, N: Oscillation of solutions of non -linear ... >  1 σ 0 + p 0 γ σ 0 τ 0  ((n − 1)!) γ e , (2:13) then every solution of (1.1) is oscillatory or tends to zero as t đ . Proof. The proof of the corollary is similar to the proof of Corollary 2.8 and so it is omitted. Example...

Ngày tải lên: 20/06/2014, 22:20

... use of Gronwall inequality. Then, v ≤ u in D T , 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 ... fund of Department of Education of Sichuan Province 10ZC127 and the research fund of Sichuan College of Education CJYKT09-024. References 1 C. V. Pao, Nonlinear Parabolic and Elliptic Equations, ... the principle of induction, we complete the proof of the lemma. 3. Uniform Estimates of {u m }, {u m } To prove the existence of solutions to 1.1, in this section, we show the uniform estimates of { u m },...

Ngày tải lên: 21/06/2014, 05:20

... to the study of stability and estimates of solutions of 1.1. 2. Exponential Stability and Estimates of the Convergence of Solutions to Stable Systems First we give two definitions of stability ... vxx T Hx has been used to investigate the stability of systems 1.1 in 5see 6 as well. The stability of linear neutral systems of type 1.1,butwithdifferent delays h 1 and h 2 ,isstudiedin1 ... also suggested for investigating the asymptotic stability of neutral nonlinear systems. The investigation of nonlinear neutral delayed systems with two time dependent bounded delays in 9 to...

Ngày tải lên: 21/06/2014, 11:20

... been an increasing interest in the study of qualitative analysis of rational difference equations and systems of difference equations. Although difference equations are very simple in form, it is ... of lyness-type difference equations, ” Advances in Difference Equations, vol. 2007, Article ID 31272, 13 pages, 2007. 12 B. Iri ´ canin and S. Stevi ´ c, “Some systems of nonlinear difference equations ... solutions of a system of two nonlinear difference equations, ” Communications on Applied Nonlinear Analysis, vol. 5, no. 2, pp. 47–59, 1998. 10 G. Papaschinopoulos and C. J. Schinas, “Invariants for systems...

Ngày tải lên: 22/06/2014, 11:20

... reducibility of 1.1 into the form of 1.5 and then obtain asymptotic stability of the zero solution of 1.1. 2. Reducible systems In this section, we give a theorem on the structure of the matrix ... Bohner We first give a theorem on the reducibility of linear system of difference equations of the form xn  1Anxn. Next, by the means of Floquet theory, we obtain some stability results. Moreover, ... “Periodic solutions of nonlinear second-order difference equations, ” Advances in Difference Equations, vol. 2005, no. 2, pp. 173–192, 2005. 3 S. N. Elaydi, An Introduction to Difference Equations, Undergraduate...

Ngày tải lên: 22/06/2014, 11:20

... and D. W. Reynolds, “On exact convergence rates for solutions of linear systems of Volterra difference equations, ” Journal of Difference Equations and Applications, vol. 12, no. 12, pp. 1257–1275, ... 2004. 11 S. Bodine and D. A. Lutz, “On asymptotic equivalence of perturbed linear systems of differential and difference equations, ” Journal of Mathematical Analysis and Applications, vol. 326, no. ... boundedness of solutions of difference Volterra equations, ” Applied Mathematics Letters, vol. 16, no. 6, pp. 857–862, 2003. 18 Z. H. Li, “The asymptotic estimates of solutions of difference equations, ”...

Ngày tải lên: 22/06/2014, 11:20

... subset of zero measure of [ −h,0]; that is, it consists of a finite set of bounded discontinuities so that it is of support of zero measure, (3) ϕ (3) :[−h,0] → R n + is either null or impulsive of ... controllability of positive systems, ” Linear Algebra and Its Applications, vol. 94, pp. 35–53, 1987. [23] V. G. Rumchev and D. J. G. James, “Controllability of positive linear discrete-time systems, ” International ... the sets of square real n -matrices and that of q-continuously differentiable square real n-matrix functions on R + .Realn -matrices and real n-matrix functions are also in the sets of linear operators...

Ngày tải lên: 22/06/2014, 18:20

... fractional system of difference equations, Radovi Matemati ˇ cki 11 (2002), no. 1, 59–78. [12] , Asymptotic behavior of a system of linear fractional difference equations, JournalofIn- equalities ... 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 that ... is a solution of (1.14), then lim n→∞ n    x n   =   λ i (A)   , i = 1, ,k, (1.17) where λ i (A) denotes one of the eigenvalues of the matrix A. 2.Proofofconjecture Proof of Conjecture...

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