Lecture Notes

Special software is required to use some of the files in this section: .m.


LEC # LECTURE NOTES SUPPLEMENTARY FILES
1

Introduction, Basic Linear Algebra (PDF)

6 slides per page (PDF)

2

Orthogonal Vectors and Matrices, Norms (PDF)

6 slides per page (PDF)

Vector Norms

lec2mldemo1.m (M)

Induced Matrix Norms

lec2mldemo2.m (M)

3

The Singular Value Decomposition (PDF)

6 slides per page (PDF)

4

The QR Factorization (PDF)

6 slides per page (PDF)

5

Gram-Schmidt Orthogonalization (PDF)

6 slides per page (PDF)

Classical and Modified Gram-Schmidt

lec5mldemo1.m (M)

clgs.m (M)

mgs.m (M)

6

Householder Reflectors and Givens Rotations (PDF)

6 slides per page (PDF)

Householder QR Factorization

house.m (M)

formQ.m (M)

7

Least Squares Problems (PDF)

6 slides per page (PDF)

8

Floating Point Arithmetic, The IEEE Standard (PDF)

6 slides per page (PDF)

Floating Point Arithmetic

lec8mldemo1.m (M)

num2bin.m (M)

9

Conditioning and Stability I (PDF)

6 slides per page (PDF)

10

Conditioning and Stability II (PDF)

6 slides per page (PDF)

11

Gaussian Elimination, The LU Factorization (PDF)

6 slides per page (PDF)

LU Factorization

lec11mldemo1.m (M)

lec11mldemo2.m (M)

mkL.m (M)

mkP.m (M)

12

Stability of LU, Cholesky Factorization (PDF)

6 slides per page (PDF)

13

Eigenvalue Problems (PDF)

6 slides per page (PDF)

14

Hessenberg / Tridiagonal Reduction (PDF)

6 slides per page (PDF)

15

The QR Algorithm I (PDF)

6 slides per page (PDF)

16

The QR Algorithm II (PDF)

6 slides per page (PDF)

Jacobi Algorithm

lec16mldemo1.m (M)

jacrot.m (M)

17

Other Eigenvalue Algorithms (PDF)

6 slides per page (PDF)

Method of Bisection

lec17mldemo1.m (M)

sturmcount.m (M)

Divide-and-Conquer Algorithm

lec17mldemo2.m (M)

18

The Classical Iterative Methods (PDF)

6 slides per page (PDF)

19

The Conjugate Gradients Algorithm I (PDF)

6 slides per page (PDF)

Conjugate Gradients

cg.m (M)

cg_stats.m (M)

20

The Conjugate Gradients Algorithm II (PDF)

6 slides per page (PDF)

Conjugate Gradients

lec20mldemo1.m (M)

steep.m (M)

conjdir.m (M)

conjgrad.m (M)

21

Sparse Matrix Algorithms (PDF)

6 slides per page (PDF)

Elimination Movie

lec21mldemo1.m (M)

realmmd.m (M)

22

Preconditioning, Incomplete Factorizations (PDF)

6 slides per page (PDF)

23

Arnoldi / Lanczos Iterations (PDF)

6 slides per page (PDF)

Arnoldi Iteration

arnoldi.m (M)

24

GMRES, Other Krylov Subspace Methods (PDF)

6 slides per page (PDF)

25

Linear Algebra Software (PDF)

6 slides per page (PDF)