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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

1996 • Question 3

Question

Math 6610 • Analysis of Numerical Methods I 1996 • Question 3

Gaussian Elimination is LU Factorization. What is the LU factorization of a square matrix? How do you solve a linear system \(Ax=b\) by Gaussian Elimination? Show that for a general \(4\times 4\) system the matrix part of Gaussian Elimination is equivalent to computing the LU factorization of \(A\).

Raw LaTeX

\textbf{Gaussian Elimination is LU Factorization.} What is the LU factorization
of a square matrix? How do you solve a linear system \(Ax=b\) by Gaussian
Elimination? Show that for a general \(4\times4\) system the matrix part of Gaussian
Elimination is equivalent to computing the LU factorization of \(A\).

Topic Tags

Cholesky Factorization and SPD Matrices Gaussian Elimination and Pivoting Iterative Methods for Linear Systems Linear Programming and Optimization