Computational Methods of Linear Algebra 1st Edition by V N Faddeeva – Ebook PDF Instant Download/Delivery. 978-0486604244 0486604241
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Product details:
ISBN 10: 0486604241
ISBN 13: 978-0486604244
Author: V. N. Faddeeva
The book consists of three chapters. In the first chapter is given the material from linear algebra that is indispensable to what follows. The second chapter is devoted to the numerical solution of systems of linear equations and parallel questions. Lastly, the third chapter contains a description of numerical methods of computing the proper numbers and proper and vectors of a matrix.
Computational Methods Of Linear 1st Table of contents:
-
Linear Systems of Equations
- Direct Methods for Solving Linear Systems
- Gaussian Elimination
- LU Decomposition
- Pivoting Techniques
- Condition Number and Stability
-
Iterative Methods
- Introduction to Iterative Solvers
- Jacobi Method
- Gauss-Seidel Method
- Successive Over-Relaxation (SOR)
- Convergence Criteria and Error Analysis
-
Matrix Factorizations and Decompositions
- QR Decomposition
- Singular Value Decomposition (SVD)
- Cholesky Decomposition
- Eigenvalue Decompositions
-
Least Squares Problems
- Introduction to Least Squares
- Solving Overdetermined Systems
- Normal Equations
- QR Factorization in Least Squares
- Applications in Data Fitting
-
Eigenvalues and Eigenvectors
- Eigenvalue Problem Formulation
- Power Method and Inverse Iteration
- QR Algorithm for Eigenvalue Computation
- Applications of Eigenvalues in Numerical Methods
-
Sparse Matrix Techniques
- Introduction to Sparse Matrices
- Storage Formats for Sparse Matrices
- Sparse Direct Solvers
- Iterative Methods for Sparse Systems
- Preconditioning Techniques
-
Linear Systems in Computational Physics and Engineering
- Application of Linear Systems in Engineering
- Computational Fluid Dynamics (CFD) Problems
- Structural Analysis and Linear Systems
- Numerical Methods for Partial Differential Equations (PDEs)
-
Optimization and Linear Programming
- Linear Programming Formulation
- Simplex Method
- Interior Point Methods
- Applications of Linear Programming in Optimization
-
Computational Methods for Large-Scale Systems
- Challenges of Solving Large-Scale Linear Systems
- Parallel Computation in Linear Algebra
- Distributed Computing for Linear Systems
- Preconditioning and Multigrid Methods
-
Applications of Linear Methods
- Linear Methods in Machine Learning and Data Science
- Graph Algorithms and Network Flow Problems
- Computer Graphics and Image Processing
- Signal Processing and Control Systems
-
Advanced Topics in Computational Linear Algebra
- Krylov Subspaces and Conjugate Gradient Methods
- Multigrid Methods for Linear Systems
- Randomized Algorithms in Linear Algebra
- Theoretical Considerations in Computational Methods
-
Case Studies and Real-World Examples
- Solving Large-Scale Systems in Practice
- Numerical Experiments and Performance Analysis
- Case Studies in Engineering, Physics, and Data Science
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