Computational Methods of Linear Algebra by V. N. Faddeeva
Computational Methods of Linear Algebra - Table of Contents
Part-I Basic material from linear algebra
1. Matrices
2. n-Dimensional vector space
3. Linear transformations
4. The Jordan canonical form
5. The concept of limit for vectors and matrices
Part-II Systems of linear equations
6. Gauss’s method
7. The evaluation of determinants
8. Compact arrangements for the solution of sacteenogeneyaes linear systems
9. The connection of Gauss’s method with the decomposition of a matrix into factors
10. The square-root method
11. The inversion of a matrix
12. The problem of elimination
13. Correction of the elements of the inverse matrix
14. The inversion of a matrix by partitioning
15. The bordering method
16. The escalator method
17. The method of iteration
18. The preparatory conversion of a system of linear equations into form suitable for the method of iteration
19. Scidel’s method
20. Comparison of the methods
Part-III The proper numbers and proper vectors of a matrix
2l. The method of A. N. Krylov
22. The determination of proper vectors by the method of A. N. Krylov
23. Samuelson’s method
24. The method of A. M. Danthcsky
25. Leverrier’s method in D. K. Faddeev’s modification
26. ‘The escalator method
27. ‘The method of interpolation
28. Comparison of the methods
29. Determination of the first proper number of a matrix, First case
30. Improving the convergence of the iterative process
31. Finding the proper numbers next in line
32. Determination of the proper numbers next in line and their proper vectors as well
33. Determination of the first proper number
34. The case of a matrix with nonlinear elementary divisors
35. Improving the convergence of the iterative process for solving systems of linear equations
What You Will Learn in Computational Methods of Linear Algebra
"Computational Methods of Linear Algebra" by V. N. Faddeeva is a classic reference that focuses on solving linear algebra problems using "numerical computation" rather than abstract theory. The book was developed during the early days of scientific computing and reflects a strong emphasis on accuracy and reliability in calculations. It is especially valuable for readers interested in practical computation.
The text covers essential topics such as solving systems of linear equations, computing "eigenvalues", and working with matrices using step-by-step algorithms. It explains methods that were designed for hand calculation and early computers, which helps readers deeply understand the logic behind modern numerical algorithms. Many examples include detailed tables that demonstrate each stage of computation clearly.
Overall, the book is well suited for mathematicians, engineers, and scientists who want a strong foundation in "numerical methods", "matrix algorithms", and "computational accuracy". While the style is traditional, the ideas remain relevant and continue to influence modern "scientific computing" and applied linear algebra.
Book Details & Specifications
Title:
Computational Methods of Linear Algebra by V. N. Faddeeva
Publisher:
Dover Publications
Year:
1959
Pages:
280
Type:
PDF
Language:
English
ISBN-10 #:
0486604241
ISBN-13 #:
978-0486604244
License:
External Educational Resource
Amazon:
Amazon
About the Author: Vera Nikolaevna Faddeeva
The author Vera Nikolaevna Faddeeva
was a pioneering mathematician who made major contributions to "numerical linear algebra", "scientific computing", and applied mathematics. She worked at the Steklov Mathematical Institute and focused on making complex matrix calculations reliable and practical for real-world use. As the author of "Computational Methods of Linear Algebra", Faddeeva helped establish key ideas in "matrix algorithms", "eigenvalue computation", and "numerical stability". Her work bridged theory and computation and continues to influence modern engineering and mathematical research.
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