Rao, in Discrete Cosine and Sine Transforms, 2007 5.2.7 QR, LU, LDU and PLUS factorizations
Therefore these methods are applicable when many large-scale mathematical models are treated.
Indeed, no special property of the matrices arising in air pollution modelling is exploited during the construction of these methods. It should be emphasized that the methods for handling sparse matrices by an attempt to exploit efficiently the cache memory of the available computer, which were discussed in the previous three sections, are very general. Moreover, as emphasized in the previous sections of this chapter, standard methods for efficient performance of different matrix computations are available and can be used in the efforts to handle efficiently different computational tasks arising when the models from Section 7 in Chapter 1 are to be treated on modern high-speed computers. Matrix computations are used in the treatment of nearly all large-scale models. The proper organization of the matrix computations is becoming more and more important when high-speed computers with hierarchical memory (based on several levels of caches) are used in the treatment of large computational tasks. Giorgio Semenza, in Studies in Computational Mathematics, 2006 6.8 Applicability to other models
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