Computational Methods of Linear Algebra by V. N. Faddeeva

Book 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

About this book :-
"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 Detail :-
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 Author :-
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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