LUP-Decomposition

• The basic principle used to write the LU decomposition algorithm and flowchart is – ““A square matrix [A] can be written as the product of a lower triangular matrix [L] and an upper triangular matrix [U], one of them being unit triangular, if all the principal minors of [A] are non-singular.”
• So, for a linear system AX = b, the given matrix [A] can be decomposed into the product two lower and upper triangular matrices.

Algorithm

• Start
• Read the elements of augmented matrix into arrays a and b
• Calculate elements of L and U
• Print elements of L and U
• Find V by solving LV = B by forward substitution
• Find X by solving UX = V by backward substitution
• Print Array X as the solution
• Stop

Steps to run program on google colab

• %%writefile filename.c[This will be written at the start of the program]
• For compiling follow this instruction
  %%shell
gcc filename.c -o output
./output