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M10 · Numerical Linear Algebra and Scientific Computing

A free, illustrated L3 course of 9 modules in the Mathematics track. Modules include: Floating point and numerical stability; LU, Cholesky and QR in practice; Conditioning and error analysis.

M10 L3 · Advanced 9 modules · about 36 lessons Planned · Ring 4

Part of the Mathematics track. Ships in Ring 4 (Expert) of the roadmap.

Modules

1. Floating point and numerical stability
2. LU, Cholesky and QR in practice
3. Conditioning and error analysis
4. Iterative solvers: conjugate gradient and GMRES
5. Eigenvalue algorithms
6. Randomized linear algebra and sketching
7. Sparse matrices and graphs
8. Numerical differentiation and integration
9. Fast transforms: FFT and convolution

Signature illustrations

The pictures a learner should still see in their head a year later:

The floating-point number line, convergence curves, sparsity patterns, randomized range-finder schematic.

Status

This course is planned, not written yet. It ships with Ring 4 (Expert).

Every lesson will follow the same twelve-part blueprint with at least three purpose-made figures. Watch the repository to hear when modules ship, or help write and review it.