24 Solving the Mixed Model Equations at Scale

Learning Objectives

By the end of this chapter, you will be able to:

Explain why direct inversion is infeasible for a national evaluation
Describe the sparsity of the MME and of A⁻¹
Implement Jacobi and Gauss–Seidel iteration on a small system
Describe PCG and iteration on data conceptually
Explain how reliabilities are approximated when the LHS cannot be inverted

Assumes Ch 6.

Chapter in progress

This chapter has not been written yet. The objectives above are the contract it will be written against — they are taken from CHAPTERS.md, which is the outline for the whole book.

Purpose. Expose students to what production software actually does. Deliberately thin.

---
title: "Solving the Mixed Model Equations at Scale"
---

::: {.callout-note icon=false}
## Learning Objectives

By the end of this chapter, you will be able to:

1. **Explain** why direct inversion is infeasible for a national evaluation
2. **Describe** the sparsity of the MME and of **A⁻¹**
3. **Implement** Jacobi and Gauss–Seidel iteration on a small system
4. **Describe** PCG and iteration on data conceptually
5. **Explain** how reliabilities are approximated when the LHS cannot be inverted
:::

*Assumes Ch 6.*

::: {.callout-warning}
## Chapter in progress

This chapter has not been written yet. The objectives above are the contract it will be written
against — they are taken from `CHAPTERS.md`, which is the outline for the whole book.

**Purpose.** Expose students to what production software actually does. Deliberately thin.
:::