This is why the LU decomposition in general looks like .

Compared to the LU decomposition, it is roughly twice as efficient.

For this reason, the LU decomposition is usually preferred.

Then, LU decomposition with partial pivoting is used for the timing.

For small matrices it is known that LU decomposition is faster.

He also invented the LU decomposition method in 1948, used today for solving matrix equations.

The LU decomposition is an excellent general purpose linear equation solver.

One way to find the LU decomposition of this simple matrix would be to simply solve the linear equations by inspection.

The LU decomposition is basically a modified form of Gaussian elimination.

LU Decomposition - A robust algorithm for solving linear equations.

The LU decomposition can be viewed as the matrix form of Gaussian elimination.

The same method readily applies to LU decomposition by setting P to the identity matrix.

The Bareiss algorithm for an LU decomposition is stable.

Turing formulated the LU decomposition method.

If the LU decomposition is used, then the algorithm is unstable unless we use some sort of pivoting strategy.

The floating point index has been left alone, it is still the geometric mean of fourier, neural net, and LU decomposition.

LU reduction is an algorithm related to LU decomposition.

The Gaussian elimination algorithm for obtaining LU decomposition has also been extended to this most general case.

Computing the LU decomposition using either of these algorithms requires 2n / 3 floating point operations, ignoring lower order terms.

The LU decomposition was introduced by mathematician Alan Turing.

Macsyma did not have many of the basic algorithms of numerical linear algebra, such as LU decomposition.

Therefore to find the unique LU decomposition, it is necessary to put some restriction on L and U matrices.

LU decomposition on MathWorld.

An alternative is the LU decomposition which generates upper and lower triangular matrices which are easier to invert.

For problems that are not too large, sparse LU decompositions and Cholesky decompositions still work well.