numerical-linear-algebra-sol

This document is a solutions manual to accompany Trefethen, Lloyd N., and David Bau III. Numerical Linear Algebra. SIAM, 1997.

All solutions are based on the author's definitions, assuming that all theorems, including lemmas and corollaries, and examples covered in the text can be cited without proof. If one quotes a proposition introduced in another exercise, see the solution to that problem for proof.

This paper is unofficial and might still contain some errors, although I have worked on minimizing them. You can contribute to it via my email. All reports and suggestions are welcome.

Solved Exercises

• Part I. Fundamentals
  • Chapter 4. The Singular Value Decomposition
    4.1, 4.2,4.4
  • Chapter 5. More on the SVD
    5.4
• Part II. QR Factorization and Least Squares
  • Chapter 6. Projectors
    6.1, 6.2, 6.4, 6.5
  • Chapter 7. QR Factorization
    7.1, 7.4, 7.5
  • Chapter 10. Householder Triangularization
    10.1, 10.4
  • Chapter 11. Least Squares Problems
    11.1
• Part III. Conditioning and Stability
  • Chapter 12. Conditioning and Condition Numbers
    12.1
  • Chapter 13. Floating Point Arithmetic
    13.1
  • Chapter 14. Stability
    14.1, 14.2
  • Chapter 15. More on Stability
    15.1, 15.2
  • Chapter 16. Stability of Householder Triangularization
    16.1
  • Chapter 17. Stability of Back Substitution
    17.2
  • Chapter 19. Stability of Least Squares Algorithms
    19.2
• Part IV. Systems of Equations
  • Chapter 20. Gaussian Elimination
    20.3, 20.4
  • Chapter 21. Pivoting
    21.1, 21.3, 21.6
  • Chapter 22. Stability of Gaussian Elimination
    22.1, 22.3
  • Chapter 23. Cholesky Factorization
    23.1
• Part V. Eigenvalues
  • Chapter 24. Eigenvalue Problems
    24.2
  • Chapter 25. Overview of Eigenvalue Algorithms
    25.3
  • Chapter 27. Rayleigh Quotient, Inverse Iteration
    27.1
  • Chapter 28. QR Algorithm without Shifts
    28.2
  • Chapter 31. Computing the SVD
    31.4
• Part VI. Iterative Methods
  • Chapter 33. The Arnoldi Iteration
    33.2
  • Chapter 35. GMRES
    35.5
  • Chapter 36. The Lanczos Iteration
    36.1
  • Chapter 38. Conjugate Gradients
    38.3, 38.5
  • Chapter 40. Preconditioning
    40.1