Tikhonov regularisation

It is proposed in [92], that the summary of polymer MWD can be nsed for the Tikhonov regularisation method [93, 94] to derive AC distribntion by chain termination probability. No assumption has been made about the type of this distribution. 

The complexity of Equation 3.43 in relation to Z(s) is because it falls into the category of improperly posed problems in this case. The numerical solution of Equation 3.43 has been obtained by the Tikhonov regularisation method the following conditions are required to obtain an approximate Z(s) solution by approximation of the right part U (x) firstly, the Z(s) value must give the residual norm not exceeding the experimental data error ... 

The solution of the inverse MWD problem using the Tikhonov regularisation method has revealed that the traditional polybutadiene polymerisation process with TiCl4-A1(2-C4H9)3 occurs in the presence of four types of AC. The location of the maximums on the kinetic inhomogeneity curves corresponds to the following intervals of MW values (each type synthesises different polymer fractions) lnM = 9.2-10.4 - Type I 11.2-11.4 - Type II 12.9-13.2 - Type III and 14.1-14.7 - Type IV. 

This is known as zeroth-order Tikhonov regularisation. See [129] for an excellent overview of deterministic inverse problem solving. The book [49] is a treatment of inverse problems from the point of view of the applied mathematician. 

When the point data values, 99, are not available then the method implied by the functional in (25) is called first-order Tikhonov regularisation for a = 0 and second-order Tikhonov regularisation for a = 1. 

In the ILT algorithm, a Tikhonov regularisation parameter (called a) is used to adapt the analysis to the quality (S/N) and the type of data. Figure 7.29 shows the influence of this a parameter on ILT results for a mature white cement paste. The parameter a was varied between what is considered as... 

The minimum of the Tikhonov functional is achieved with the optimal value of the a regularisation parameter a = 9A x 10, while the residual norm value was 1.07x1This method allows the variation of the error value in the integral equation core selection process. However, as the model core was the Schulz-Flory function, the error h was assumed to be h 0. 

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