Computational Methods of Linear Algebra by V. N. Faddeeva
Computational Methods of Linear Algebra - Table of Contents
PART I: BASIC LINEAR ALGEBRA & LINEAR SYSTEMS
- 1. Matrices and Vector Spaces
- 2. Linear Transformations and Jordan Form
- 3. Limits for Vectors and Matrices
- 4. Gauss’s Method and Matrix Factorizations
- 5. Square-Root Method and Elimination
- 6. Matrix Inversion and Partitioning Schemes
- 7. The Bordering and Escalator Methods
- 8. Iterative Methods and Seidel Iteration
PART II: EIGENVALUES & EIGENVECTORS
- 9. The Method of A. N. Krylov
- 10. Samuelson and Danilevsky Methods
- 11. Leverrier Method in D. K. Faddeev’s Modification
- 12. Escalator and Interpolation Methods
- 13. Determination of Proper Numbers and Vectors
- 14. Matrices with Nonlinear Elementary Divisors
- 15. Convergence Acceleration Methods
What You Will Learn in Computational Methods of Linear Algebra
Computational Methods of Linear Algebra by V. N. Faddeeva is an authoritative, historically significant masterpiece that established the foundations of numerical matrix computations and linear system algorithms. This comprehensive volume guides readers through matrix factorizations, Gauss elimination, matrix inversion methods, Seidel iterations, and Krylov subspace eigensolvers with exceptional mathematical depth and structural clarity.
Designed for graduate students, numerical analysts, computational mathematicians, and theoretical physicists, this foundational text bridges pure linear algebra and early high-performance algorithmic design. Faddeeva details step-by-step hand-computation arrangements, iterative acceleration schemes, and matrix bordering methods for solving large systems of linear equations. Whether you are analyzing matrix condition numbers, computing matrix inverses, or deriving proper values and vectors, this classic work offers an indispensable roadmap.
Recognized globally as a cornerstone of 20th-century computational mathematics, it remains one of the best classical matrix computation books for self-study. By balancing analytical matrix theory with concrete numerical techniques, it serves as an essential tool for mastering computational linear algebra with confidence.
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
(1906–1983) was a distinguished Soviet mathematician renowned worldwide for her pioneering contributions to numerical linear algebra and computational mathematics. A prominent researcher at the Steklov Institute of Mathematics in Leningrad, she worked closely alongside her husband, the eminent algebraist D. K. Faddeev, to develop foundational matrix algorithms and numerical techniques.
First published in 1950, Faddeeva's Computational Methods of Linear Algebra was among the earliest comprehensive monographs devoted to matrix calculations, setting international standards for the field. Her precise mathematical exposition, emphasis on algorithmic organization, and rigorous error analysis make this text a classic reference for classical matrix computations that continues to inspire numerical analysts globally.
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