Matrix Decomposition Selection Guide
Run the Selection Guide Fullscreen
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About This MicroSim
This interactive decision tree helps you choose the right matrix decomposition for your problem. Click on blue decision nodes to explore different paths, and green nodes show the recommended decomposition with reasoning.
Decision Summary
| Goal | Matrix Type | Recommended |
|---|---|---|
| Solve Ax=b | Symmetric positive definite | Cholesky |
| Solve Ax=b | Square, invertible | LU with pivoting |
| Solve Ax=b | Rectangular | QR or SVD |
| Least squares | Any overdetermined | QR |
| Low-rank approx | Any | Truncated SVD |
| Eigenvalues needed | Any | SVD |
How to Use
- Start at the top "Start" node
- Click on blue question nodes to explore paths
- Read the green answer nodes for recommendations
- Hover over nodes to see explanations
Learning Objectives
After using this MicroSim, students will be able to:
- Match problems to appropriate decompositions
- Understand why certain decompositions are preferred
- Navigate the decision tree efficiently
- Justify decomposition choices
Quick Reference
When to Use Each Decomposition
| Decomposition | Best For | Complexity |
|---|---|---|
| Cholesky | SPD systems, fastest | O(n³/3) |
| LU | Square systems, multiple b's | O(2n³/3) |
| QR | Least squares, rectangular | O(2mn²) |
| SVD | Low-rank, rank analysis | O(mn²) |
References
- Chapter 7: Matrix Decompositions - Choosing the Right Decomposition