Improving Speed of Solving Linear Equations by LU Method in LabVIEW and Producing Special CIN
Hao Shang-hua
Abstract
Hao Shang-hua
Abstract
The method of improving the speed of solving linear equations by LU method in LabVIEW was introduced.There are four kinds of situations for the system of linear equations,namely,coefficient matrix is upper triangle or lower triangle or positive matrix or no nonsingular matrix.When it is upper triangle,the elements in coefficient matrix's diagonal of augmented matrix are united and the linear equations can be solved easily.When it is lower triangle,the lower triangle is transformed into upper triangle and then the linear equations are solved.When it is positive matrix,the coefficient matrix is decomposed by LU method and solved again.For the fourth situation,it will not be judged whether the linear equations have the solution,or the linear equations are not solved.Finally,according to this algorithm,the author wrote the C codes and gave the steps of producing CIN.
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The method of improving the speed of solving linear equations by LU method in LabVIEW was introduced.There are four kinds of situations for the system of linear equations,namely,coefficient matrix is upper triangle or lower triangle or positive matrix or no nonsingular matrix.When it is upper triangle,the elements in coefficient matrix's diagonal of augmented matrix are united and the linear equations can be solved easily.When it is lower triangle,the lower triangle is transformed into upper triangle and then the linear equations are solved.When it is positive matrix,the coefficient matrix is decomposed by LU method and solved again.For the fourth situation,it will not be judged whether the linear equations have the solution,or the linear equations are not solved.Finally,according to this algorithm,the author wrote the C codes and gave the steps of producing CIN.
Key concepts: Coefficient matrix, Invertible matrix, Matrix (chemical analysis), Mathematics, Linear equation, System of linear equations, Triangular matrix, Augmented matrix