International Tables for Crystallography (2006). Vol. C, ch. 8.1, pp. 678-688
doi: 10.1107/97809553602060000609

Chapter 8.1. Least squares

Contents

  • 8.1. Least squares  (pp. 678-688) | html | pdf | chapter contents |
    • 8.1.1. Definitions  (pp. 678-680) | html | pdf |
      • 8.1.1.1. Linear algebra  (pp. 678-679) | html | pdf |
      • 8.1.1.2. Statistics  (pp. 679-680) | html | pdf |
    • 8.1.2. Principles of least squares  (pp. 680-681) | html | pdf |
    • 8.1.3. Implementation of linear least squares  (pp. 681-682) | html | pdf |
      • 8.1.3.1. Use of the QR factorization  (pp. 681-682) | html | pdf |
      • 8.1.3.2. The normal equations  (p. 682) | html | pdf |
      • 8.1.3.3. Conditioning  (p. 682) | html | pdf |
    • 8.1.4. Methods for nonlinear least squares  (pp. 682-685) | html | pdf |
      • 8.1.4.1. The Gauss–Newton algorithm  (p. 683) | html | pdf |
      • 8.1.4.2. Trust-region methods – the Levenberg–Marquardt algorithm  (p. 683) | html | pdf |
      • 8.1.4.3. Quasi-Newton, or secant, methods  (pp. 683-684) | html | pdf |
      • 8.1.4.4. Stopping rules  (pp. 684-685) | html | pdf |
      • 8.1.4.5. Recommendations  (p. 685) | html | pdf |
    • 8.1.5. Numerical methods for large-scale problems  (pp. 685-687) | html | pdf |
      • 8.1.5.1. Methods for sparse matrices  (pp. 685-686) | html | pdf |
      • 8.1.5.2. Conjugate-gradient methods  (pp. 686-687) | html | pdf |
    • 8.1.6. Orthogonal distance regression  (pp. 687-688) | html | pdf |
    • 8.1.7. Software for least-squares calculations  (p. 688) | html | pdf |
    • References | html | pdf |