Adaptive algorithm

The multiresolution framework allows us to reconsider more constructively some of the features of the structure adaptation algorithm. First, a strictly forward move in the ladder of subspaces [Eq. (8)] is not necessary. Due to localization, the structural correction can be sought in higher spaces before ail functions in the previous space are exhausted. This... 

Studied in another publication (Koulouris and Stephanopoulos, 1995). Some computational details and variations of the adaptation algorithm have also to be evaluated to improve the efficiency of the computations. 

In situ adaptive tabulation (IS AT) was proposed by Pope (1997), and it overcomes many of the difficulties associated with pre-computed lookup tables. First, the in situ nature of the method reduces the tabulation to only those points that occur during a particular simulation (i.e., the accessed region). Secondly, an adaptive algorithm is employed to control interpolation errors while minimizing the number of points that must be tabulated. 

G.R. Platen, R.M. Belchamber, M. Collins, A.D. Walmsley, Caterpillar - an adaptive algorithm for detecting process changes from acoustic emission signals. Anal. Chim. Acta, 544, 280-291 (2005). 

The mesh-adaptation algorithm implemented in Twopnt [158] forms the next-finer mesh by adding points to the current coarser mesh. It adds mesh points in regions where the solution has high gradient and high curvature on the current coarser-mesh solution. Between every two mesh points ( j, j — 1), the following criteria are evaluated for each of the n solution components,... 

Constant associated with solution gradient in mesh adaption algorithm ... 

L. Frediani, R. Cammi, C. S. Pomelli, J. Tomasi and K. Ruud, New developments in the symmetry-adapted algorithm of the polarizable continuum model, J. Comput. Chem., 25 (2004) 375-385. 

Abstract An improvement is made to an automatic quadrature due to Ninomiya (J. Inf. Process. 3 162-170, 1980) of adaptive type based on the Newton-Cotes rule by incorporating a doubly-adaptive algorithm due to Favati, Lotti and Romani (ACM Trans. Math. Softw. 17 207-217,1991 ACM Trans. Math. Softw. 17 218-232, 1991). We compare the present method in performance with some others by using various test problems including Kahaner s ones (Computation of numerical quadrature formulas. In Rice, J.R. (ed.) Mathematical Software, 229-259. Academic, Orlando, FL, 1971). 

A doubly-adaptive method [3,7,11,12] is both order and partition adaptive [16]. This scheme chooses either to apply the order adaptive method to the current subinterval or to further split the subinterval, by detecting the local regularity of the integrand. An improved version QXG (QXGS) due to Favati, Lotti and Romani [5] (we call FLR henceforth) of QAG (QAGS) is a doubly-adaptive algorithm based on recursive monotone stable (RMS) formulas [4, 6]. Ninomiya s method is less effective for oscillatory integrands than the FLR method. 

Figure 7.13. The variation of window sizes as a result of the adaptive algorithm. Prom [286], reproduced with permission. Copyright 2003 AIChE.

C Jutten and J Herault. Blind separation of sources I. An adaptive algorithm based on neuromimetric architecture. Signal Process., 24 1, 1991. 

In this study, the work in adaptive algorithms for realistic controllers is divided between LMS-based approaches and direct optimization approaches. The difference is in the amount of a priori information required for the controller. In the LMS case, a model of the control to error path over the relevant bandwidth is required [3]. In current implementation, this model is identified in real time when the controller is first turned on. 

Evesque, S., A. P. Dowling, and A. M.. Annaswamy. 2000. Adaptive algorithms for control of combustion. NATO/RTO Active Control Symposium Proceedings. Braunschweig, Germany. 

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