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Non-linear problems

Plotting ln(y) versus time t results in a straight line with slope -k and intercept ln(Io). These two parameters can be computed non-iteratively in a linear regression. The program could look like this  [Pg.127]

This task can be problematic as the correct value for const is not necessarily accurately known. Subtracting a wrong value obviously results in a flawed analysis, and this is not always easily detected. [Pg.129]

It is worthwhile noting that if a smaller amount of noise is added to the y-data, the subtraction of the wrong constant offset manifests in a visible curvature of their logarithmic plot. This in turn could be misinterpreted as non-exponential behaviour. [Pg.129]


Theoretical analysis of convergence in non-linear problems is incomplete and in most instances does not yield clear results. Conclusions drawn from the analyses of linear elliptic problems, however, provide basic guidelines for solving non-linear or non-elliptic equations. [Pg.33]

Christie, I. et al., 1981. Product approximation for non-linear problems in the finite element method. IMA J. Numer. Anal 1, 253-266. [Pg.108]

Levenberg, K., "A Method for the Solution of Certain Non-linear Problems in Least Squares", Quart. Appl. Math., 11(2), 164-168 (1944). [Pg.397]

Chapter 4, Model-Based Analyses, is essentially an introduction into least-squares fitting. It is crucial to clearly distinguish between linear and nonlinear least-squares fitting linear problems have explicit solutions while non-linear problems need to be solved iteratively. Linear regression forms the base for just about everything and thus requires particular consideration. [Pg.4]

In general, non-linear problems cannot be resolved explicitly, i.e. there is no equation that allows the computation of the result in a direct way. Usually such systems can be resolved numerically in an iterative process. In most instances, this is done via a truncated Taylor series expansion. This downgrades the problem to a linear one that can be resolved with a stroke of the brush or the Matlab / and commands see The Pseudo-Inverse (p.ll 7). [Pg.48]

As with almost any other non-linear problem that has to be solved iteratively, linearisation via a Taylor expansion with truncation after very few elements, is the solution. [Pg.148]

We do not design our own algorithm here but use the fin Insearch. m function supplied by Matlab. It is based on the original Nelder, Mead simplex algorithm. As an example, we re-analyse our exponential decay data Data Decay. m (see p. 106], this time fitting both parameters, the rate constant and the amplitude. Compare the results with those from the linearisation of the exponential curve, followed by a linear least-squares fit, as performed in Linearisation of Non-Linear Problems, (p.127). [Pg.205]

Burke and his students (11) have published a proposal for solving the non-linearity problem associated with CC and the consequent correlation noise. They used a constant frequency multiple injection signal while this occurred, this frequency was modulated. Before each injection, a random number was generated to determine the magnitude and sign of the deviation from the carrier frequency for the next injection time. Thus, the next... [Pg.96]

Irradiated Crystals, Nuclear Quadrupole Resonance in (Duchesne). Irreversible Processes, Non-linear Problems in Thermodynamics of... [Pg.384]

Note that, by using the quasi-linearization method, the solution of a non-linear problem can be reduced to solution of a succession of linear problems. The method is a further development of the Newton-Raphson method (Dulnev and Ushakovskaya, 1988) and its generalized version. [Pg.306]

K. Levenberg. A method for the solution of certain non-linear problems in least squares. The Quarterly of Applied Mathematics, 2 164—168, 1944. [Pg.67]

The resistance matrix depends on co-ordinates of all particles, in nonlinear manner. The situation is illustrated in Appendix F for the case of two particles. To avoid the non-linear problem, one uses the preliminary averaging of the hydrodynamic resistance matrix (Kirkwood and Riseman 1948 Zimm... [Pg.27]

The boundary value problem (Eqs. (10), (11)) is usually solved numerically. However, it is also possible to use another approach employing a linearization of this second-order, non-linear problem and a subsequent analytical treatment The analytical solution of the linearized boundary value problem in the film region is obtained in [15] ... [Pg.284]

Equations are solved sequentially using an iterative solver. The technique is inherently suited for solving non-linear problems, where non-linearity arises either from material behaviour, geometry or boundary conditions. [Pg.201]


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See also in sourсe #XX -- [ Pg.252 ]




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