Jeff Liu Lab
Home
Projects
Workshop
AI Wiki
AI Lab
Shop
中
Sign In
All
Computing Science
Artificial Intelligence
Deep Learning
Reinforcement Learning
AI Agents
Embodied Intelligence
Robot Engineering
Human-Like Intelligence
AI Engineering
← Back to Wiki
Computing Science
Mathematical Foundations
Calculus
Linear Algebra
Probability Theory
Information Theory
Statistics
Automatic Differentiation
Discrete Mathematics
Numerical Methods
Optimization Theory
Graph Theory Fundamentals
Theory of Computation
Algorithms
Computer Architecture
Operating Systems
Computer Networks
Programming Languages
Software Engineering
Comments (0)
Sign in to comment
Table of Contents
1. Floating-Point Representation and Error
1.1 IEEE 754 Floating Point
1.2 Types of Error
2. Interpolation
2.1 Lagrange Interpolation
2.2 Newton Interpolation
2.3 Spline Interpolation
3. Numerical Integration
3.1 The Trapezoidal Rule
3.2 Simpson's Rule
3.3 Gaussian Quadrature
4. Linear Systems
4.1 Gaussian Elimination
4.2 LU Decomposition
4.3 Iterative Methods
5. Nonlinear Root Finding
5.1 The Bisection Method
5.2 Newton's Method
5.3 The Secant Method
6. Numerical Solutions of ODEs
6.1 Euler's Method
6.2 The Runge-Kutta Method (RK4)
6.3 Stiff Problems and Implicit Methods
7. Numerical Stability
7.1 Condition Number
7.2 Backward Error Analysis
8. Applications in AI
8.1 Neural ODEs
8.2 Physics-Informed Neural Networks (PINNs)
8.3 Numerical Linear Algebra and Deep Learning
References
Comments
Comments (0)
Sign in to comment