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Mathematical Methods For Robotics And Vision by Carlo Tomasi (2000).pdf

CS 205
Mathematical Methods for Robotics and Vision
Carlo Tomasi
Stanford University
Fall 2000
D.L.
1. Introduction
2. Unknown numbers
2.1 Algebraic linear systems
2.1.1 Characterization of the solutions to a linear system
2.1.2 Gaussian elimination
2.1.3 The Singular Value Decomposition
2.1.4 The pseudoinverse
2.2 Function optimization
2.2.1 Newton and Gauss-Newton methods
2.2.2 Levenberg-Marquardt method
2.2.3 Constraints and Lagrange multipliers
3. Unknown functions of one real variable
3.1 Ordinary differential linear systems
3.1.1 Eigenvalues and eigenvectors
3.1.2 The Schur decomposition
3.1.3 Ordinary differential linear systems
3.1.4 The matrix zoo
3.1.5 Real, symmetric, positive-definite matrices
3.2 Statistical estimation
3.2.1 Linear estimation
3.2.2 Weighted least squares
3.2.3 The Kalman filter
4. Unknown functions of several variables
4.1 Tensor fields of several variables
4.1.1 Grad, div, curl
4.1.2 Line, surface, and volume integrals
4.1.3 Green’s theorem and potential fields of two variables
4.1.4 Stokes’ and divergence theorems and potential fields of three variables
4.1.5 Diffusion and flow problems
4.2 Partial differential equations and sparse linear systems
4.2.1 Finite differences
4.2.2 Direct versus iterative solution methods
4.2.3 Jacobi and Gauss-Seidel iterations
4.2.4 Successive overrelaxation

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