{R}R 開発ノート

合計 5 件の記事が見つかりました。

4.3 Pivoting Strategies

A practical and intuitive guide to pivoting strategies in numerical linear algebra, explaining partial, complete, and scaled pivoting and why pivoting is essential for stable Gaussian elimination and reliable LU decomposition.

2025-09-20

4.2 Row Operations and Elementary Matrices

A deep but intuitive explanation of row operations and elementary matrices, showing how Gaussian elimination is built from structured matrix transformations and how these transformations form the foundation of LU decomposition and numerical stability.

2025-09-19

4.1 Gaussian Elimination Revisited

A deep, intuitive exploration of Gaussian elimination as it actually behaves inside floating-point arithmetic. Learn why the textbook algorithm fails in practice, how instability emerges, why pivoting is essential, and how elimination becomes reliable through matrix transformations.

2025-09-18

4.0 Solving Ax = b

A deep, accessible introduction to solving linear systems in numerical computing. Learn why Ax = b sits at the center of AI, ML, optimization, and simulation, and explore Gaussian elimination, pivoting, row operations, and failure modes through intuitive explanations.

2025-09-17

1.0 Why Numerical Linear Algebra Matters

A deep, practical introduction to why numerical linear algebra matters in real AI, ML, and optimization systems. Learn how stability, conditioning, and floating-point behavior impact models.

2025-09-02

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