Abstract
In this chapter we first review Gaussian elimination. Gaussian elimination leads to an LU factorization of the coefficient matrix or more generally to a PLU factorization, if row interchanges are introduced. Here P is a permutation matrix, L is lower triangular and U is upper triangular.
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Notes
- 1.
The method was known long before Gauss used it in 1809. It was further developed by Doolittle in 1881, see [4].
- 2.
Hint: Consider the cases 2 ≤ k ≤ d and d + 1 ≤ k ≤ n separately.
References
J.F. Grcar, Mathematicians of gaussian elimination. Not. AMS 58, 782–792 (2011)
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Lyche, T. (2020). Gaussian Elimination and LU Factorizations. In: Numerical Linear Algebra and Matrix Factorizations. Texts in Computational Science and Engineering, vol 22. Springer, Cham. https://doi.org/10.1007/978-3-030-36468-7_3
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DOI: https://doi.org/10.1007/978-3-030-36468-7_3
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