Topic Number Topics Related Readings
1 linear algebra review: span, linear dependence, bases, matrices, matrix-vector multiplication, matrix-matrix multiplication, column space, rank, outer product matrices, matrix range and nullspace Solomon 1.1-1.3
2 Floating point number representation Floating point math, sources of error Solomon 2.1-2.3 , Heath 1.2-1.3
3 Linear systems, Existence and uniqueness of solutions Solomon 3.1, Heath 2.1-2.2
4 triangular systems, forward/backward substitution, LU factorization Solomon 3.2-3.5, Heath 2.4
5 Special linear systems, positive definite matrices, Cholesky factorization, sparse matrices Solomon 4.2, Heath 2.5
6 matrix and vector norms, sensitivity analysis, conditioning, and stability Solomon 4.3 , Heath 2.3
7 Orthogonality, orthonormal set of vectors, orthogonal matrix, projections Solomon 5.1-5.3
8 Gram-Schmidt, modified Gram-Schmidt, Householder transformations Solomon 5.4-5.6, Heath 3.5
9 Singular Value Decomposition, pseudoinverse, fundamental subspaces of A Solomon 7, Heath 3.6
10 Least squares problems, normal equations Heath 3.1-3.4
11 Least squares by QR, Tikhonov regulariation of LS, weighted LS Solomon 4.1.2-4.1.3, Heath 3.5-3.7
12 Eigenvectors, characteristic polynomial Solomon 6.1-6.2, Heath 4.1-4.3
13 Eigenvalues, similarity, defective matrices, Schur form Solomon 6.1-6.2, Heath 4.4-4.5
14 iterative methods, convergence rates examples: Jacobi iteration, Gauss-Seidel iteration Heath 5.4
15 Power iteration, inverse power iteration, shifting, QR iteration Solomon 6.3-6.4, Heath 4.5
16 Nonlinear equations, root finding, bisection method Solomon 8.1, Heath 5.1-5.5
17 Fixed point iteration, Newton's method, single variable Solomon 8.1, Heath 5.5
18 Systems of nonlinear equations, Newton's method for systems Solomon 8.2-8.3, Heath 5.6
19 Unconstrainted optimization, optimality Solomon 9.1-9.2, Heath 6.1-6.5