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In this work a technique has been developed to solve a set of nonlinear equations with the assumption that a solution exists. The algorithm involves nonlinear Gauss-Seidel iteractions and at each iteration the value of the iterate is added to a predetermined perturbation parameter which is computed in terms of quantities already known. This perturbation parameter has two properties: (i) it determines the mode of convergence, that means it shows how many more computations are required so that convergence may be achieved, and (ii) it accelerates the rate of convergence. The algorithm is computationally simple. Several nonlinear equations have been studied. The results seem to be encouraging.  相似文献   

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In this work we present the explicit expression of all rectangular Toeplitz matrices B,C which verify the equation BBH+CCH=aI for some a>0. This matrix equation arises in some signal processing problems. For instance, it appears when designing the even and odd components of paraunitary filters, which are widely used for signal compression and denoising purposes. We also point out the relationship between the above matrix equation and the polynomial Bézout equation |B(z)|2+|C(z)|2=a>0 for |z|=1. By exploiting this fact, our results also yield a constructive method for the parameterization of all solutions B(z),C(z). The main advantage of our approach is that B and C are built without need of spectral factorization. Besides these theoretical advances, in order to illustrate the effectiveness of our approach, some examples of paraunitary filters design are finally given.  相似文献   

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The purpose of this paper is to examine the controllability for a class of nonlinear control systems of the form $$\frac{{d\phi t}}{{dt}} = X_0 (\phi t) + \sum\limits_{j = 1}^r {u_j (t)X_j } (\phi _t )$$ Our general theorem is stated in terms of differential geometry, but it will be applied to concrete systems such that coefficientsX 0,..,X r are polynomials.  相似文献   

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We give some sufficient conditions for the continuation of solutions for some nonlinear differential equations. As an application, we obtain a new criterion for the oscillation of solutions of the Liénard equation.  相似文献   

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Known results for linear difference equations mod 2 with T-periodic solutions are extended and compiled for applications to the semicycle analysis of nonlinear difference equations. For the calculation of T, four methods are presented. A further application concerns rational functions in the field of integers mod 2.  相似文献   

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Summary We introduce a martingale problem to associate diffusion processes with a kind of nonlinear parabolic equation. Then we show the existence and uniqueness theorems for solutions to the martingale problem.Research partially supported by the Air Force Office of Scientific Research Contract No. F4962082C0009  相似文献   

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The solution of a class of nonlinear singular integro-differential equations with Carleman shift is obtained in the space Hμ(n)(Γ). The approach followed depends essentially on solution of linear singular integro-differential equation with shift. A criterion for the Noetherity of a correspondence singular integral functional operator of second order with Carleman shift preserving orientation is obtained and the index formula is given.  相似文献   

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A recently proposed method for the derivation of exact analytical integral formulae for the zeros of analytic functions (based on the simple discontinuity problem for a sectionally analytic function along the real axis) is applied here to the case of polynomials. The peculiarity of the present application is that the integrals appearing in the closed-form formulae for the sought zeros are interpreted as Cauchy-type principal-value integrals or even as finite-part integrals. The case of the quintic equation with real coefficients is considered in some detail, and it is shown that the roots of this equation can always be obtained in closed form. Numerical results for this equation are also presented. Equations of higher degree can also be solved in closed form under appropriate conditions.  相似文献   

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一类强阻尼非线性波动方程的广义解   总被引:1,自引:0,他引:1  
用Galerkin方法研究了一类非线性波动方程的初边值问题,证明其在一定条件下强解的存在性.  相似文献   

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