Optional Advanced Topics

These topics extend the core workflow. They should be introduced after participants can distinguish conditioning, stability, validation, and reproducibility.

Mixed-precision computation

Choosing precision per operation or data structure, analyzing error propagation, and validating performance-driven precision changes.

Arbitrary precision and interval arithmetic

Using higher precision as an investigative tool and intervals as bounds, while understanding their cost and limitations.

Numerical linear algebra

Condition estimation, rank decisions, pivoting, scaling, iterative refinement, and residual-based diagnostics.

Stochastic algorithms

Seeds, ensembles, statistical tests, uncertainty in estimated quantities, and statistical rather than bitwise reproducibility.

Accelerator and distributed computing

Reduction order, fused operations, device-specific precision, compiler flags, communication topology, and scalable reproducibility strategies.

Domain-specific case studies

The general workflow can be applied to simulation, optimization, data analysis, signal processing, computational chemistry, machine learning, and other institute-relevant domains.