Learn · Numerical Linear Algebra
Lecture 20 of 60Unit-4
Computer Representation of Numbers
Prof. P.N. Agrawal Prof. D. N Pandey · IIT Roorkee
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- From
- Numerical Linear Algebra, IIT Roorkee (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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- Tweens profiles and older. How courses are placed
All the lectures
- Matrix Operations and Types of Matrices
- Determinant of a Matrix
- Rank of a Matrix
- Vector Space-I
- Vector Space-II
- Linear dependence and independence
- Bases and Dimension - I
- Bases and Dimension - II
- Linear Transformation - I
- Linear Transformation - II
- Orthogonal Subspaces
- Row Space, Column Space and Null Space
- Eigen Values & Eigen Vectors-I
- Eigen Values & Eigen Vectors-II
- Diagonalizable Matrices
- Orthogonal Sets
- Gram Schmidt ortthogonalization and orthogonal bases
- Introduction to Matlab
- Sign Integer Representation
- Computer Representation of Numbers
- Floating Point Representation
- Round-off Error
- Error Propagation in Computer Arithmetic
- Addition and Multiplication of Floating Point Numbers
- Conditioning and Condition Numbers-I
- Conditioning and Condition Numbers-II
- Stability of Numerical Algorithms-I
- Stability of Numerical Algorithms-II
- Vector Norms - I
- Vector Norms - II
- Matrix Norms - I
- Matrix Norms - II
- Convergent Matrices - I
- Convergent Matrices - II
- Stability of non linear system
- Condition number of a matrix: Elementary Properties
- Sensitivity Analysis-I
- Sensitivity Analysis-II
- Residual Theorem
- Nearness to Singularity
- Estimation of the Condition Number
- Singular value decomposition of a matrix - I
- Singular value decomposition of a matrix - II
- Orthonormal Projections
- Algebraic and geometric properties of SVD
- SVD and their applications
- Perturbation theorem for singular values
- Outer product expansion of a matrix
- Least square solutions - I
- Least square solutions - II
- Householder matrices
- Householder matrices and their applications
- Householder QR factorization- I
- Householder QR factorization- II
- Basic theorems on eigenvalues and QR method
- Power Method
- Rate of Convergence of Power Method
- Applications of Power Method with Shift
- Jacobi Method-I
- Jacobi Method-II