what are LU decomposition applications in engineeringSolutio

what are LU decomposition applications in engineering?

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Signal processing is an area of system engineering, electrical engineering and applied mathematics that deals with the operations on or analysis of analog as well as digitized signal, representing time varying or spatially physical quantities. There are various mathematical model applied in signal processing such as linear time invariant system, system identification, optimization, estimation theory, numerical methods .In the computational application matrix decomposition is a basic operation. “Matrix decomposition refers to the transformation of the given matrix into a given canonical form”. Matrix factorization is the process of producing the decomposition where the given matrix is transformed to right hand side product of canonical matrices Matrix decomposition is a fundamental theme in linear algebra and applied statis tics which has both scientific and engineering significance. Computational convenience and analytic simplicity are the two main aspects in the purpose of matrix decomposition. In the real world it is not feasible for most of the matrix computation to be calculated in an optimal explicit way such as matrix inversion, matrix determinant, solving linear systems and least square fitting , thus to convert a difficult matrix computation problem into several easier task such as solving triangular or diagonal systems will greatly facilitate the calculations. Data matrices such as proximity matrix or correlation matrix represent numerical observations and it is often huge and hard to analyze them. Therefore to decompose the data matrices into some lower rank canonica l forms will reveal the inherent characteristics. Since matrix computation algorithms are expensive computational tasks, hardware implementation of these algorithms require substantial time and effort. There is an increasing demand for domain specific tool for matrix computation algorithms which provide fast and highly efficient hardware production. In this paper there is review of matrix decomposition techniques that are used in signal processing.