Standard syllabus
Numerical linear algebra · Graduate · Math
Topics
Matrix factorizations and direct methods
- Review of LU, QR, and Cholesky factorizations
- Pivoting strategies and backward stability analysis
- Sherman–Morrison–Woodbury and low-rank updates
- Sparse direct solvers: fill-in and reordering (overview)
- Block algorithms and cache efficiency (introduction)
Iterative methods for linear systems
- Krylov subspace methods: CG, MINRES, GMRES
- Preconditioners: Jacobi, SSOR, incomplete factorizations
- Convergence theory for SPD systems
- Nonsymmetric systems and flexible Krylov variants
- Restart strategies and breakdown remedies
Eigenvalue and SVD computations
- Power method, inverse iteration, and Rayleigh quotient
- QR algorithm and Francis shifts
- Lanczos and Arnoldi processes
- Singular value decomposition algorithms
- Pseudospectra and sensitivity of eigenvalues (introduction)
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$1,162 · Numerical linear algebra · 18 tutoring hrs
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