Iterative problems solving

Figure 16.1 Schematic of iterative problem solving process as given by the quality principles.

Emphasize iterative problem solving, e.g., design, test, redesign... 

When the Gauss-Newton method is used to estimate the unknown parameters, we linearize the model equations and at each iteration we solve the corresponding linear least squares problem. As a result, the estimated parameter values have linear least squares properties. Namely, the parameter estimates are normally distributed, unbiased (i.e., (k )=k) and their covariance matrix is given by... 

The value of this approach is that a running expert system is rapidly created, without forcing the expert to articulate a general problem-solving procedure. The prototype system is available for the iterative knowledge refinement process, which draws out more details of the decision-making procedure from the expert to gradually build a complete and tested exi>ert system. 

Root cause analysis (RCA) is a class of problem solving methods aimed at identifying the root causes of problems or events. The practice of RCA is predicated on the belief that problems are best solved by attempting to correct or eliminate root causes, as opposed to merely addressing the immediately obvious symptoms. By directing corrective measures at root causes, it is hoped that the likelihood of problem recurrence will be minimized. However it is recognized that complete prevention of recurrence by a single intervention is not always possible. Thus RCA is often considered to be an iterative process and is frequently viewed as a tool of continuous improvement. 

With this implicit boundary-condition specification, the eigenvalue computation can be easily incorporated into a Newton iteration to solve the entire problem. Time marching and adaptive meshing can also be incorporated [158,159]. 

The matrix in front of T is the partitioned orbital Hessian. Equation (4 37) is not very practical, since it involves the inverse of the Cl part of the Hessian. But suppose that we work in a configuration basis (I0>, K>), where a is diagonal, that is we start each iteration by solving the Cl problem to all orders. The matrix a is then diagonal with the matrix elements =(EK - Eq),... 

It can also be appreciated that an increment in the number of particles in the global version of the PSO code does not help the code to find a better solution for the optimization problem. This could indicate that the PSO code only needed a minimum number of particles and the inclusion of more particles will not be helpful. A different behaviour was encountered in the local version of the PSO. When more particles were used for the solution of the problem, then the code required less number of iterations to solve the problem. 

A step-wise, iterative, approach to problem solving can be illustrated as in Fig. 

In one problem-solving process, illustrated by the image of the key and its lock, the maxim is to modify a designed target structure little by little until the corresponding target molecule has the very properties of interest. It involves an iterative procedure, usually of several rounds, based on trial and error. It is trivial to note that the screening can take place only after the synthesis. 

Another problem-solving methodology popular with lean thinkers is the PDCA problem-solving loop. PDCA (plan-do-check-act) is an iterative four-step problem-solving process typically used in business process improvement. It is also known as the Demlng cycle, Shewhart cycle, Deming wheel, or Plan-Do-Study-Act. 

In all problems solved using iterative methods, it is important to define a criterion to stop the evaluations either when a reasonable approximation of the solution is achieved or when convergence is impossible. 

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