## Math 391 Numerical Linear Algebra

### Lecture Notes

The lecture notes are written in Matlab script format. You may download
them to your computer and then publish them using Matlab.

Lecture 6: IEEE Floating Point Standard
Lecture 7: Avoiding overflow, catastrophic cancellation, rearranging the recurrence
Lecture 8: Efficiency and Stability of an Algorithm
Lecture 9: Conditioning of a problem and condition numbers
Lecture 10: Condition number of a matrix and perturbation analysis of the linear system
Lecture 11: Gaussian Elimination
Lecture 12: Gaussian Elimination with Partial Pivoting
Lecture 13: Cholesky Factorizatin for Positive Definite Matrices
Lecture 14: Linear System with Special Matrices, Inverses, Determinants
Lecture 15: QR Factorization and Householder Triangularization
Lecture 16: Givens Rotation and QR Factorization
Lecture 17: Singular Value Decomposition and Its Properties
Lecture 18: Least Squares Problem
Lecture 19: Minimum-Norm Least Squares Solution
Lecture 20: Eigenvalue Problems
Lecture 21: Rayleigh Quotient, Power Iteration, Rayleigh Quotient Iteration
lecture22: QR Algorithm for Eigenvalue Problems and SVD

### Matlab Code

Gaussian Elimination A=LU
Back Substitution for solving Rx=b
Gaussian Elimination with Partial Pivoting PA=LU
Cholesky Factorization
A=LU for Hessenberg Matrices
A=LU for Tridiagonal Matrices
Householder Reflection for QR Factorization
Form Q explicitly for A=QR
Multiply Q with a given vector implicitly
Multiply Q^T with a given vector implicitly
Solve Ax=b using QR factorization
Compute the (minimum-norm) (least squares) solution to Ax=b using SVD
Power Iteration
Inverse Iteration
Rayleigh Quotient Iteration
Testing Rayleigh Quotient Iteration

Solution to quiz 3
Solution to problem 2 of quiz 5