{R}R 開発ノート

合計 8 件の記事が見つかりました。

8.3 The QR Algorithm (High-Level Intuition)

A clear, intuitive, and comprehensive explanation of the QR algorithm—how repeated QR factorizations reveal eigenvalues, why orthogonal transformations provide stability, and how shifts and Hessenberg reductions make the method efficient. Ends with a smooth bridge to PCA and spectral methods.
2025-10-09

7.3 Least Squares Problems

A clear, intuitive, book-length explanation of least squares problems, including the geometry, normal equations, QR decomposition, and SVD. Learn why least-squares solutions are central to ML and data science, and why QR provides a stable foundation for practical algorithms.
2025-10-04

7.2 Householder Reflections

A clear, intuitive, book-length explanation of Householder reflections and why they form the foundation of modern QR decomposition. Learn how reflections overcome the numerical instability of Gram–Schmidt and enable stable least-squares solutions across ML, statistics, and scientific computing.
2025-10-03

3.4 Exact Algorithms vs Implemented Algorithms

Learn why textbook algorithms differ from the versions that actually run on computers. This chapter explains rounding, floating-point errors, instability, algorithmic reformulation, and why mathematically equivalent methods behave differently in AI, ML, and scientific computing.
2025-09-16

3.1 Norms and Why They Matter

A deep yet accessible exploration of vector and matrix norms, why they matter in numerical computation, and how they influence stability, conditioning, error growth, and algorithm design. Essential reading for AI, ML, and scientific computing engineers.
2025-09-13

Chapter 3 — Computation & Mathematical Systems

A clear, insightful introduction to numerical computation—covering norms, error measurement, conditioning vs stability, and the gap between mathematical algorithms and real implementations. Essential reading for anyone building AI, optimization, or scientific computing systems.
2025-09-12

2.4 Vector and Matrix Storage in Memory

A clear, practical guide to how vectors and matrices are stored in computer memory. Learn row-major vs column-major layout, strides, contiguity, tiling, cache behavior, and why memory layout affects both speed and numerical stability in real systems.
2025-09-11

Numerical Linear Algebra: Understanding Matrices and Vectors Through Computation

Learn how linear algebra actually works inside real computers. A practical guide to LU, QR, SVD, stability, conditioning, and the numerical foundations behind modern AI and machine learning.
2025-09-01

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