determinants matrices and linear systems of equations

... 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 ... Annals of Mathematics, 160 (2004), 1141–1182 Isomonodromy transformations of linear systems of difference equations By Alexei Borodin Abstract We introduce and study “isomonodromy” transformations of...

Ngày tải lên: 14/02/2014, 17:20

... 348 Chapter Root Finding and Nonlinear Sets of Equations Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright ... scaled axes, can save you a lot of grief as you enter the world of root finding 350 Chapter Root Finding and Nonlinear Sets of Equations for (i=1;i

Ngày tải lên: 07/11/2013, 19:15

... known to be within an interval of size n , then after the next iteration it will be bracketed within an interval of size 354 Chapter Root Finding and Nonlinear Sets of Equations #include ... interval into n equally spaced segments, and search for zero crossings of the function nb is input as the maximum number of roots sought, and is reset to the number of bracketing pairs xb1[1 nb], xb2[1 ... trade@cup.cam.ac.uk (outside North America) a x2 x3 b x1 d c f e 351 9.1 Bracketing and Bisection 352 Chapter Root Finding and Nonlinear Sets of Equations #include #define FACTOR 1.6 #define NTRY 50 if...

Ngày tải lên: 15/12/2013, 04:15

... REFERENCES AND FURTHER READING: Ralston, A., and Rabinowitz, P 1978, A First Course in Numerical Analysis, 2nd ed (New York: McGraw-Hill), §8.3 Ostrowski, A.M 1966, Solutions of Equations and Systems of ... Method, False Position Method, and Ridders’ Method f(x) 356 Chapter Root Finding and Nonlinear Sets of Equations f (x) Figure 9.2.3 Example where both the secant and false position methods will ... rtf; Convergence } nrerror("Maximum number of iterations exceeded in rtflsp"); return 0.0; Never get here 358 Chapter Root Finding and Nonlinear Sets of Equations Ridders’ Method f(x1 ) − 2f(x3...

Ngày tải lên: 15/12/2013, 04:15

... Finding and Nonlinear Sets of Equations } a=b; fa=fb; if (fabs(d) > tol1) b += d; else b += SIGN(tol1,xm); fb=(*func)(b); Move last best guess to a Evaluate new trial root } CITED REFERENCES AND ... estimate of the root and P/Q ought to be a “small” correction Quadratic methods work well only when the function behaves smoothly; they run the serious risk of giving very bad estimates of the ... keep track of whether a supposedly superlinear method is actually converging the way it is supposed to, and, if it is not, we can intersperse bisection steps so as to guarantee at least linear convergence...

Ngày tải lên: 15/12/2013, 04:15

... and Nonlinear Sets of Equations of the desired root But that means that in the neighborhood of an extremum there must be a tiny, perhaps distorted, copy of the basin of convergence — a kind of ... the superlinear order of √ convergence will be only (ii) If you take dx too small you will be wiped out by roundoff, while if you take it too large your order of convergence will be only linear, ... evaluated efficiently, and whose derivative is continuous and nonzero in the neighborhood of a root Even where Newton-Raphson is rejected for the early stages of convergence (because of its poor global...

Ngày tải lên: 15/12/2013, 04:15

... 370 Chapter Root Finding and Nonlinear Sets of Equations f (x) f (x) (a) x (b) Figure 9.5.1 (a) Linear, quadratic, and cubic behavior at the roots of polynomials Only under high magnification ... roots of arbitrary polynomials You can easily verify (see, e.g., [6]) that the characteristic polynomial of the special m × m companion matrix 376 Chapter Root Finding and Nonlinear Sets of Equations ... must be off the real axis, otherwise you will never get off that axis — and may get shot off to infinity by a minimum or maximum of the polynomial For real polynomials, the alternative means of polishing...

Ngày tải lên: 15/12/2013, 04:15

... Root Finding and Nonlinear Sets of Equations no root here! two roots here f pos g pos M f=0 g pos g= g neg f pos f neg g neg = g g= g pos x Figure 9.6.1 Solution of two nonlinear equations in ... vector of values xi and F denote the entire vector of functions Fi In the neighborhood of x, each of the functions Fi can be expanded Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC ... sums of squares of the individual functions Fi to get a master function F which (i) is positive definite, and (ii) has a global minimum of zero exactly at all solutions of the original set of nonlinear...

Ngày tải lên: 15/12/2013, 04:15

... Globally Convergent Methods for Nonlinear Systems of Equations The routine newt assumes that typical values of all components of x and of F are of order unity, and it can fail if this assumption ... Nonlinear Systems of Equations 393 More Advanced Implementations CITED REFERENCES AND FURTHER READING: Dennis, J.E., and Schnabel, R.B 1983, Numerical Methods for Unconstrained Optimization and ... (i=1;i

Ngày tải lên: 15/12/2013, 04:15

... References Hansen, E and Sengupta, S.: Bounding solutions of systems of equations using interval analysis BIT 21, 203–211 (1981) Neumaier, A.: Interval Methods for Systems of Equations Cambridge ... Discrete abstractions of hybrid systems Proceeding of IEEE 88, 970–983 (2000) Nedialkov, N.S., Mohrenschildt, M.v.: Rigorous Simulation of Hybrid Dynamic Systems with Symbolic and Interval Methods ... Modeling of Hybrid Systems Using Interval Arithmetic Constraints Hybrid Systems: Computation and Control, 139–142 (2004) Ishii D., Ueda K., Hosobe H., and Goldsztejn A.: Interval-based Solving of Hybrid...

Ngày tải lên: 12/01/2014, 22:20

... Institutions have more and highly diversified candidates and students Need for distinct teaching and learning approaches and environments Need for changes in systems and institutions Council of Europe, Public ... OPPORTUNITIES IN OPEN AND DIVERSIFIED SYSTEMS OF HIGHER EDUCATION Developments of Higher Education in Europe The past forty years • Driving forces and processes – Responding to increasing demand and economic ... forces and processes “Important ideological similarity between the reforms of the 1960s and 1970s and those of the 1980s and 1990s Both based on the regognition that higher education is of great...

Ngày tải lên: 31/03/2014, 07:20

... properties of nonnegative matrices and their permanents, Soviet e Math Dokl 14:945-949 (1973) [4] R A Brualdi, J L Goldwasser and T S Michael, Maximum permanents of matrices of zeroes and ones, ... Minc, Theory of permanents 1978-1981, Linear and Multilinear Algebra 12:227-263, (1983) [13] A Schrijver, Bounds on permanents, and the number of 1-factors and 1-factorizations of bipartite graphs, ... w) Proof: We prove only (a) and (b); the proofs of (c) and (d) being similar Let {λi }n i=1 be the roots of ρ(R, x), labelled in non-decreasing order Suppose x is in the interval (k, λn ) and choose...

Ngày tải lên: 07/08/2014, 06:22

... (shoot and root) and root and shoot ratios in the garrigue of Southern France Kummerow et al [22], Rambal [32] and Rambal and Leuterne [33] evaluated and analyzed the characteristics of the root systems ... the scarcity of data, and lack of precision in the methodology used Thus there is no global theory which explains the dynamic and structural relations of root systems in natural ecosystems the ... and browse biomass The purpose of the present study is to contribute with quantitative data to the generally scarce knowledge of Q coccifera root and shoot systems and their ratio The shrubland...

Ngày tải lên: 08/08/2014, 14:22

Ngày tải lên: 01/02/2015, 23:46

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 ... where P and Q are positive matrices and γ is a positive scalar Delay independent criteria of stability for some classes of delay neutral systems are developed in 10 The stability of systems ... 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...

Ngày tải lên: 21/06/2014, 11:20

... SJS−1 , then the k-average of A is SJ S−1 , where J is the k-average of J J is in turn composed of the k-average of each of its Jordan blocks For a Jordan block of J of the form ⎞ λ ⎟ ⎜ ⎟ ⎜ λ ... completes the proof of part a Suppose that A satisfies the conditions in b and that A SJS−1 is the Jordan canonical form of A Let λ be an eigenvalue of A and let v be a column vector of S corresponding ... applications of preceding theorems to approximation of solution of a linear system Ax b, where A ∈ Mn and b a given vector in Cn Let Q be a given invertible b if and only if x is a fixed point of the...

Ngày tải lên: 21/06/2014, 20:20

... reducibility of 1.1 into the form of 1.5 and then obtain asymptotic stability of the zero solution of 1.1 Reducible systems In this section, we give a theorem on the structure of the matrix S n , and ... ≤ and the eigenvalues of unit modulus are semisimple; ii asymptotically stable if and only if ρ A < 1, where ρ A of A} is the spectral radius of A max{|λ| : λ is an eigenvalue Consider the linear ... Kipnis and D Komissarova, “Stability of a delay difference system,” Advances in Difference Equations, vol 2006, Article ID 31409, pages, 2006 V Lakshmikantham and D Trigiante, Theory of Difference Equations: ...

Ngày tải lên: 22/06/2014, 11:20

... versions of E defined in (23) Therefore, the upper bound on ergodic capacity of a frequency-selective channel is a function of the sum of eigenvalue matrices of spatial correlation matrices of different ... the effect of eigenvalues distribution of spatial and path correlation matrices on the capacity of frequency-flat and -selective channels Next, we introduced a linear scheme known as linear precoding ... Institute of Electrical and Electronics Engineers (IEEE), a Fellow of the Engineering Institute of Canada (EIC), and a Fellow of the Canadian Academy of Engineering (CAE) He is the recipient of the...

Ngày tải lên: 22/06/2014, 19:20