Numerical Linear Algebra with Applications: Using MATLAB and Octave, Second Edition provides practical knowledge on modern computational techniques for the numerical solution of linear algebra problems. The book offers a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions. Useful to readers regardless of background, the text begins with six introductory courses to provide background for those who haven’t taken applied or theoretical linear algebra. This approach offers a thorough explanation of the issues and methods for practical computing using MATLAB as the vehicle for computation.
Appropriate for advanced undergraduate and early graduate courses on numerical linear algebra, this useful textbook explores numerous applications to engineering and science.
1. Title of Book - p. i 2. Cover image - p. i 3. Title page - p. ii 4. Table of Contents - p. iii 5. Copyright - p. iv 6. Dedication - p. v 7. List of figures - p. xiii 8. Preface - p. xvii 9. Acknowledgments - p. xxv 10. Chapter 1: Matrices - p. 1 11. Chapter 2: Linear equations - p. 29 12. Chapter 3: Subspaces - p. 53 13. Chapter 4: Determinants - p. 67 14. Chapter 5: Eigenvalues and eigenvectors - p. 89 15. Chapter 6: Orthogonal vectors and matrices - p. 115 16. Chapter 7: Vector and matrix norms - p. 133 17. Chapter 8: Floating-point arithmetic - p. 161 18. Chapter 9: Algorithms - p. 181 19. Chapter 10: Conditioning of problems and stability of algorithms - p. 199 20. Chapter 11: Gaussian elimination and the LU decomposition - p. 225 21. Chapter 12: Linear system applications - p. 263 22. Chapter 13: Important special systems - p. 287 23. Chapter 14: Gram–Schmidt orthonormalization - p. 307 24. Chapter 15: The singular value decomposition - p. 325 25. Chapter 16: Least squares problems - p. 349 26. Chapter 17: Implementing the QR decomposition - p. 385 27. Chapter 18: The algebraic eigenvalue problem - p. 415 28. Chapter 19: The symmetric eigenvalue problem - p. 481 29. Chapter 20: Basic iterative methods - p. 515 30. Chapter 21: Krylov subspace methods - p. 539 31. Chapter 22: Large sparse eigenvalue problems - p. 583 32. Chapter 23: Computing the singular value decomposition - p. 601 33. Appendix A: Complex numbers - p. 619 34. Appendix B: Mathematical induction - p. 629 35. Appendix C: Chebyshev polynomials - p. 633 36. Glossary - p. 637 37. Bibliography - p. 645 38. Index - p. 647
Numerical Linear Algebra with Applications: Using MATLAB and Octave, Second Edition provides practical knowledge on modern computational techniques for the numerical solution of linear algebra problems. The book offers a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions. Useful to readers regardless of background, the text begins with six introductory courses to provide background for those who haven’t taken applied or theoretical linear algebra. This approach offers a thorough explanation of the issues and methods for practical computing using MATLAB as the vehicle for computation.
Appropriate for advanced undergraduate and early graduate courses on numerical linear algebra, this useful textbook explores numerous applications to engineering and science.
1. Title of Book - p. i 2. Cover image - p. i 3. Title page - p. ii 4. Table of Contents - p. iii 5. Copyright - p. iv 6. Dedication - p. v 7. List of figures - p. xiii 8. Preface - p. xvii 9. Acknowledgments - p. xxv 10. Chapter 1: Matrices - p. 1 11. Chapter 2: Linear equations - p. 29 12. Chapter 3: Subspaces - p. 53 13. Chapter 4: Determinants - p. 67 14. Chapter 5: Eigenvalues and eigenvectors - p. 89 15. Chapter 6: Orthogonal vectors and matrices - p. 115 16. Chapter 7: Vector and matrix norms - p. 133 17. Chapter 8: Floating-point arithmetic - p. 161 18. Chapter 9: Algorithms - p. 181 19. Chapter 10: Conditioning of problems and stability of algorithms - p. 199 20. Chapter 11: Gaussian elimination and the LU decomposition - p. 225 21. Chapter 12: Linear system applications - p. 263 22. Chapter 13: Important special systems - p. 287 23. Chapter 14: Gram–Schmidt orthonormalization - p. 307 24. Chapter 15: The singular value decomposition - p. 325 25. Chapter 16: Least squares problems - p. 349 26. Chapter 17: Implementing the QR decomposition - p. 385 27. Chapter 18: The algebraic eigenvalue problem - p. 415 28. Chapter 19: The symmetric eigenvalue problem - p. 481 29. Chapter 20: Basic iterative methods - p. 515 30. Chapter 21: Krylov subspace methods - p. 539 31. Chapter 22: Large sparse eigenvalue problems - p. 583 32. Chapter 23: Computing the singular value decomposition - p. 601 33. Appendix A: Complex numbers - p. 619 34. Appendix B: Mathematical induction - p. 629 35. Appendix C: Chebyshev polynomials - p. 633 36. Glossary - p. 637 37. Bibliography - p. 645 38. Index - p. 647
