Special Topics in Graphics: Numerical Method (Foundations, ML, Visual Computing)
Course ID 15769
Description Many problems in machine learning, visual computing, robotics, and mechanics lack exact analytical solutions. Numerical computing provides powerful techniques to approximate these solutions using computational methods, combining applied math and programming to solve real-world problems such as simulation, optimization, and data analysis. The course begins with a review on calculus and linear algebra, followed by an introduction to how numbers are represented on computers and error analysis. It then moves on to core topics, including matrix factorization, solving linear and nonlinear systems, optimization, and numerical solution of differential equations. Students will gain hands-on experience developing numerical algorithms and learn to balance accuracy, stability, and efficiency in problem-specific contexts, such as image processing, physics-based animation, motion planning and control, structural analysis, etc.
Key Topics
numerical representation;
error analysis;
interpolation;
numerical differentiation;
numerical integration;
linear and nonlinear systems;
matrix factorization;
numerical optimization;
numerical solution of ODEs and PDEs;
Required Background Knowledge
strong math and programming skills
Course Relevance
sophomore and above
Course Goals
Understand and apply core numerical methods for solving mathematical problems.
Analyze and mitigate errors in computational solutions.
Implement and optimize algorithms for linear algebra, optimization, and differential equations.
Use numerical methods to solve real-world challenges in machine learning and scientific computing.
Learning Resources
https://people.csail.mit.edu/jsolomon/share/book/numerical_book.pdf
Assessment Structure
Weekly Assignments: 75% (7.5% each)
In-Class Midterm Exam: 10%
In-Class Final Exam: 15%
Extra Time Commitment
n/a
Course Link
https://www.cs.cmu.edu/~15369-f25/