nawidgc said:Is it possible to obtain a solution of the linear system Ax = b with LU decomposition when A contains zeros on its diagonal? I am trying to obtain a solution with LU decomposition and then perform a forward/backward substitution but I get NaN entries in the solution vector x. The condition number of my matrix is 10^8. Appreciate any help/comments.
The LU decomposition method is a technique used to solve systems of linear equations by factorizing a matrix into a lower triangular matrix (L) and an upper triangular matrix (U). It is also known as LU factorization or LU solve.
The presence of zeros on the diagonal of the matrix in LU solve is a result of the Gaussian elimination process. This process aims to reduce the original matrix into an upper triangular matrix, and sometimes, zeros appear on the diagonal during this process.
No, LU solve can only be used for matrices that are non-singular, meaning they have a non-zero determinant. If a matrix has zeros on the diagonal and is non-singular, it can still be solved using LU decomposition method.
LU solve is different from other methods, such as Gaussian elimination or Cramer's rule, because it involves breaking down the original matrix into two triangular matrices, making it more efficient and accurate for larger systems of equations.
Yes, LU solve can be used for matrices with complex numbers. The decomposition process is the same, but the calculations involve complex arithmetic instead of just real numbers.