This project was an excercise for the lecture Numerical Mathematics for Bachelor students by Prof. Dr. Blank at the University of Regensburg in 2014. It implements the Doolittle algorithm (in German "Spaltenpivotisierung") for LU decomposition (with partial pivoting) of a given matrix and the solution of a linear equation system herewith.
For a matrix A the algorithm yields a permutation of rows P (can be written as vector) and a matrix B, s.t. taking
- L the part of B below the diagonal (the latter inclusive) and
- U the part of B above the diagonal (the latter inclusive)
then PA=LU and all entries of L have absolute value lower than 1. See also the description in the corresponding script of the lecture.
You will need gcc and make. Then simply call
makeThe output program lu_decomposition will, after calling it with
./lu_decomposition- ask for the input of a dimension and a square matrix of this dimension
- print the single steps for LU decomposition of this matrix (i.e. the permutation vector P and the state of B)
- ask for the input of a vector b
- print the single steps for the solution of the linear equation system Ax=b with the LU decomposition from above, using forward and backward substitution.
See also the comments in the source files.
Mind the (quite elaborate) comments in the source files that try to describe the functionality.
- LU decompositions:
lu_decomposition.* - Solution of linear equation systems:
substitutions.* - Main function:
main.* - Input, memory allocation, output:
input.*,print.*