lu-decomposition-with-pivoting's Introduction
First part of project: I used algorithm that was shared us in slide. Second part of project: I used three for loops passing rows and columns. At the beginning of the second part of project, I realised that I must pass every columns two times. Because firstly I had to pass for sorting and appliying permutation matrix for each columns. Secondly I had to pass for elemantary matrix for each column. Note that for loops only pass lower triangular of matrix.. for(j...) passing columns --------------------------------------------------------------------------------------------------------------- for(i...) passing rows Detecting max value of j. Storing row index of max value. end of i --------------------------------------------------------------------------------------------------------------- Creating permutation matrix: Row interchange operation at identity matrix between row index of max value and index of pivot location (always j). Importat point: Row index of pivot is always equal to j. Because pivot is at the j=i line. Multiplying permutation matrix with A matrix. ---------------------------------------------------------------------------------------------------------------- for(i...) passing rows Creating elemenatry matrix Creating inverse of elemenatry matrix end of i ---------------------------------------------------------------------------- Multiplying elementary matrix with A matrix. end of j -------------------------------------------------------------------------------------- Note that I used three dimenisonal matrix to store permutation matrices, elementary matrices and their inverses. j=0 j=1 j=2 i=0 a b c i=1 d e f i=2 g k l
lu-decomposition-with-pivoting's People
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