Awesome

Numerical-Linear-Algebra

Numerical Linear Algebra, Trefethen and Bau, 1997. <br> My solutions to exercises in Numerical Linear Algebra by Trefethen and Bau. <br> There may be errors or wrong solutions, so use it only for reference. <br>

Contents

I. Fundamentals

• Lecture 1. Matrix-Vector Multiplication
• Lecture 2. Orthogonal Vectors and Matrices
• Lecture 3. Norms
• Lecture 4. The Singular Value Decomposition
• Lecture 5. More on the SVD

II. QR Factorization and Least Squares

• Lecture 6. Projectors
• Lecture 7. QR Factorization
• Lecture 8. Gram-Schmidt Orthogonalization
• Lecture 9. MATLAB
• Lecture 10. Householder Triangularization
• Lecture 11. Least Squares Problems

III. Conditioning and Stability

• Lecture 12. Conditioning and Condition Numbers
• Lecture 13. Floating Point Arithmetic
• Lecture 14. Stability
• Lecture 15. More on Stability
• Lecture 16. Stability of Householder Triangularization
• Lecture 17. Stability of Back Substitution
• Lecture 18. Conditioning of Least Squares Problems
• Lecture 19. Stability of Least Squares Algorithms

IV. Systems of Equations

• Lecture 20. Gaussian Elimination
• Lecture 21. Pivoting
• Lecture 22. Stability of Gaussian Elimination
• Lecture 23. Cholesky Factorization

V. Eigenvalues

• Lecture 24. Eigenvalue Problems
• Lecture 25. Overview of Eigenvalue Algorithms
• Lecture 26. Reduction to Hessenberg or Tridiagonal Form
• Lecture 27. Rayleigh Quotient, Inverse Iteration
• Lecture 28. QR Algorithm without Shifts
• Lecture 29. QR Algorithm with Shifts
• Lecture 30. Other Eigenvalue Algorithms
• Lecture 31. Computing the SVD

VI. Iterative Methods

• Lecture 32. Overview of Iterative Methods
• Lecture 33. The Arnoldi Iteration
• Lecture 34. How Arnoldi Locates Eigenvalues
• Lecture 35. GMRES
• Lecture 36. The Lanczos Iteration
• Lecture 37. From Lanczos to Gauss Quadrature Skip
• Lecture 38. Conjugate Gradients
• Lecture 39. Biorthogonalization Methods Skip
• Lecture 40. Preconditioning