Special software is required to use some of the files in this section: .m.
Lecture notes files.
| LEC # |
LECTURE NOTES |
SUPPLEMENTARY FILES |
| 1 |
Introduction, Basic Linear Algebra (PDF)
6 slides per page (PDF)
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| 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)
|
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| 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)
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|
| 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)
|
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| 10 |
Conditioning and Stability II (PDF)
6 slides per page (PDF)
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| 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)
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| 13 |
Eigenvalue Problems (PDF)
6 slides per page (PDF)
|
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| 14 |
Hessenberg / Tridiagonal Reduction (PDF)
6 slides per page (PDF)
|
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| 15 |
The QR Algorithm I (PDF)
6 slides per page (PDF)
|
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| 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)
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| 22 |
Preconditioning, Incomplete Factorizations (PDF)
6 slides per page (PDF)
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| 23 |
Arnoldi / Lanczos Iterations (PDF)
6 slides per page (PDF)
|
Arnoldi Iteration
arnoldi.m (M)
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| 24 |
GMRES, Other Krylov Subspace Methods (PDF)
6 slides per page (PDF)
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| 25 |
Linear Algebra Software (PDF)
6 slides per page (PDF)
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