Patent ID: 7065545
Filing Date: 2006-06-20
Classification: G06F

Abstract:
1. A computer method of solving a system of linear equations of the general form [A][X]=[B], by means of a digital computer, comprising the steps of: (a) representing the linear equations system in said digital computer in the form of an extended matrix [A|B], formed by N×N+1 elements a (b) selecting a first row of elements of said matrix having a first element different from zero; (c) normalizing the values of the elements of said first row by dividing all elements of said first row by the value of the first non-zero element; (d) setting the initial value of a first index “e”, associated with the sequential order of selection of the rows, to 2; (e) selecting a second row of said matrix; (f) calculating the values of the elements of a transformation vector [K] according to the formula: where “n” is a second index associated with the sequential order of the n-th element of the vector [K] being calculated and “e” is said first index associated with the sequential index of the row being transformed; (g) transforming the values of each of the elements of the selected second row by performing the dot product of said vector [K] and a vector formed by those “e” elements of each column of the extended matrix [A|B] corresponding to the rows that have been transformed prior to the selection of said second row; (h) determining whether element a (i) if element a (j) selecting a third row of said extended matrix and repeating steps (f) to (h) until a row is found with a nonzero element a (k) normalizing row “e” by dividing all elements of row “e” by the value of said element a (l) determining from the value of said first index “e” whether all rows of said matrix have been transformed; if all rows have not been transformed, then modifying the value of said index “e” so that another row of said extended matrix is selected; (m) repeating steps (e) to (j) until all rows of said matrix have been transformed; thereby obtaining an upper diagonal matrix [U] with all elements u (n) sequentially back-substituting the value of the nth element of vector [x] according to the following formula: for i=n−1, n−2, . . . 1; whereby the calculated vector [x] is the solution vector of the original system of linear equations.