# Questions tagged [lu-decomposition]

Questions regarding the numerical method LU decomposition to decompose a matrix into the multiplication of two triangular matrices: A lower triangle matrix and an upper triangular matrix

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### Banded Matrix LU Decomposition

I have an $n$ by $n$ $k$-banded matrix for which I calculated the LU decomposition via Matlab. Now, I want to solve the system to find the resulting vector and compare the operation count with another ...
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### Is the LU decomposition just Gauss-Jordan elimination?

I am watching Gilbert Strang's neat lecture on the LU decomposition, which is taught just after Gaussian elimination. $LU$ for a matrix $A$ was found doing $EA=U$ and finally $A=E^{-1}U$. Seems to me, ...
1 vote
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### Missing the point of LU factorization / decomposition

Gaussian Elimination The system of linear equations $Ax = b$ may be solved by using Gaussian Elimination (GE) arriving to a Row Echelon Form R of the augmented matrix $[A b]$, and then using back-...
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### QR decomposition with R having values with alternating signs on diagonal

Suppose a real-valued n × n matrix A has a QR decomposition A = QR, where Q is an orthogonal matrix, and R is an upper triangular matrix. Give a method that uses this decomposition to construct ...
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### LU factorisation of a tridiagonal matrix using MATLAB

I am trying to create a function called function [l, d, u] = tridiag_factorlu(A). It takes as argument a general tridiagonal matrix A, which is stored as a normal ...
1 vote
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### Decomposing a matrix that has duplicate columns using PA=LU factorization

I am given the following matrix. $$A = \begin{bmatrix} 3 & 3 & 9 & 6 \\ 4 & 4 &4 &4 \\ 1 & 1 & 5 & 5 \\ 2 & 2 & 4 & 6\end{bmatrix}$$ As you can notice,...
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### LU Decomposition without Gaussian Elimination

I'm creating a program to compute the LU factorization of a matrix, and I was wondering if there was a way to compute an LU factorization without using Gaussian Elimination. I'm mainly worried about ...
1 vote
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### Efficient LU decomposition of matrix after updating diagonal

I am computing LU decomposition of $(kD + A)$ where $D$ is diagonal matrix with {$d_{1}$, $d_{2}$, ... , $d_{n}$}, $A$ is a real symmetric positive-definite matrix, $k$ is a number that changes on ...
1 vote
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### Is there any situation where the LDU decomposition is the same as the eigenvalue decomposition?

I was just wondering if there are any situation where the LDU decomposition is the same as eigenvalue decomposition (diagonalization)? The only way this can be possible if L and U are inverse so ...
1 vote
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### DU decomposition

My professor said that we can't express a square matrix as a product of upper triangular matrix and lower triangular although it can be expressed as a product of lower triangle matrix and an upper ...
1 vote
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### Example of regular tridiagonal matrix $A$ with given properties

I am looking for a regular tridiagonal matrix $A$ such that at the LU-decomposition with partial column pivoting the matrices $L$ and $U$ are also tridiagonal, but with total pivoting the matrices $L$ ...
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### Diagonal entries of $U$ in $LU$ factorisation of positive definite matrix

Let $A\in M(n,\mathbb R)$ be a symmetric positive definite matrix. Let $L$ be a lower triangular matrix with real entries, all whose diagonal entries are $1$ and $LA$ is upper triangular. Then, is it ...
I was asked to find the LU decomposition of $$\begin{bmatrix}5&4\\-2&-3\\\end{bmatrix}$$ I know that the shortcut method means finding the upper and using the multiplier to find the lower. In ...
### Calculate number of eigenvalues in interval $[-2, 3>$ of matrix $A$ using Sylvesters law of inertia and $LDL^T$ decomposition.
I have a new one, and I am not sure about a few things. I hoped you might help me in understanding them. For matrix  A=\left[ \begin{matrix} 4 & 4 & 0 \\ 4 & 6 & 2 \\ 0 & 2 & ...