# Questions tagged [lu-decomposition]

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30 questions
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### LU decomposition of matrix product

Let $A_1=L_1U_1$ and $A_2=L_2U_2$ be two matrices with their respective LU-factorizations ($L_i$ is lower triangular and $U_i$ upper triangular). Is it possible to obtain the LU decomposition of the ...
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### Given the Cholesky decomposition of $A$, compute efficiently Cholesky decomposition of $RAR^T$?

Let $B = RAR^T$, where $A$ is positive definite and symmetric, and $R$ a generic matrix (possibly rectangular). Suppose I know the Cholesky decomposition $A=LL^T$. Is it possible to compute the ...
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### Numerical analysis, pivoting and incomplete LU decomposition

When doing LU decomposition, the algorithm will break down if any of the diagonal element $x_{ii}$ is zero. Therefore, we can use pivoting on the matrix such that $x_{ii}$ is no longer zero. That is, ...
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### Updating Cholesky decomposition when deleting one row and one and column.

I found the answer of updating Updating Cholesky decomposition when deleting one row and one and column on Cholesky decomposition when deleting one row and one and column. Is there any generalisation ...
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### LU/LUP decomposition: can some of U's diagonal elements be zero?

I'm learning LUP decomposition. So far I've wrote Doolittle implementation in GNU Octave: ...
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### Cost of LU decomposition of a Symmetric Matrix

I have this question: what is the cost of computing LU decomposition for a symmetric matrix. I tried to compute it, however, I calculated it as $2n^2$ as follows: I considered the LDL decomposition, ...
I found this example both in class and in a book, but I'm struggling to understand why is the regular LU decomposition problematic here. Given a matrix A=\left(\matrix{1 & 0 & 0 & 0 &...
Theorem 2.3 here says that if $A$ is normal it has a positive semi-definite square root. Isn't this wrong? In particular the fourth sentence of the proof claims the eigenvalues of normal matrices are ...