Block Relaxation Algorithms in Statistics -- Part III
Project
1.
Background
1.1.
Introduction
1.2.
Analysis
1.2.1.
Semi-continuities
1.2.2.
Directional Derivatives
1.2.3.
Differentiability and Derivatives
1.2.4.
Taylor's Theorem
1.2.5.
Implicit Functions
1.2.6.
Necessary and Sufficient Conditions for a Minimum
1.3.
Point-to-Set Maps
1.3.1.
Continuities
1.3.2.
Marginal Functions
1.3.3.
Solution Maps
1.4.
Basic Inequalities
1.4.1.
Jensen's Inequality
1.4.2.
The AM-GM Inequality
1.4.3.
Cauchy-Schwartz Inequality
1.4.4.
Young's Inequality
1.5.
Fixed Point Problems and Methods
1.5.1.
Subsequential Limits
1.6.
Convex Functions
1.6.1.
Composition
1.7.
Rates of Convergence
1.7.1.
Over- and Under-Relaxation
1.7.2.
Acceleration of Convergence of Fixed Point Methods
1.8.
Matrix Algebra
1.8.1.
Eigenvalues and Eigenvectors of Symmetric Matrices
1.8.2.
Singular Values and Singular Vectors
1.8.3.
Canonical Correlation
1.8.4.
Eigenvalues and Eigenvectors of Asymmetric Matrices
1.8.5.
Modified Eigenvalue Problems
1.8.6.
Quadratics on a Sphere
1.8.7.
Generalized Inverses
1.8.8.
Partitioned Matrices
1.9.
Matrix Differential Calculus
1.9.1.
Matrix Derivatives
1.9.2.
Derivatives of Eigenvalues and Eigenvectors
1.10.
Miscellaneous
1.10.1.
Multidimensional Scaling
1.10.2.
Cobweb Plots
2.
Notation
3.
Bibliography
4.
What's New
5.
Workflow
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Block Relaxation Algorithms in Statistics -- Part III
Matrix Differential Calculus