Computation Methods in Linear Algebra

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• LU-Factorization
• Solution of TriangularSystems
• Gauss Transformation and LU-Factorization
• QR Factorization
• Householder Reflection
• Givens Rotations
• Householder QR Factorization
• Givens QR Factorization
• Main Theorem of QR Factorization
• Singular Value Decomposition
• Existence of Singular Value Decomposition
• Properties of Singular Value Decomposition
• Algorithm of Singular Value Decomposition
• Pseudoinverse Matrix
• Least-Squares Method
• Pseudoinverse Matrix and Optimum Solution
• Jordan Form of a Matrix
• Matrix Diagonalization
• Analysis of Jordan Form of a Matrix
• Algorithm of Filipov
• Strict Methods of Solving Linear Algebraic Systems of Equations
• LDM^T Decomposition and LDL^T Decomposition of a Matrix
• Positive Definite Systems
• Positive Semidefinite Matrices
• Polar Decomposition of a Matrix and Method of Square Roots
• Systems with Band Matrices
• Block Systems
• Solution of the Systems of Equations by QR Method
• Iterative Solution of Systems of Equations
• Powers of a Matrix and Inverse Matrix
• Jacobi's and Gauss-Seidel Method
• Decomposition of the System Matrix and Convergence of the Iterative process
• Acceleration of the Convergence of an Iterative Process
• Numeric Stability
• Singular Value Decomposition and Numeric Stability
• Taylor Development
• Strict Estimations
  

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