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Session 12
Numerical Computation

Computational Complexity and Algorithm Optimality

3.5 hours
Duration
8
Materials
6
Objectives
Session Overview

Advanced analysis of computational complexity for numerical algorithms including information-based complexity, optimal algorithms, and lower bounds for numerical problems.

Learning Objectives
By the end of this session, you should be able to:
  • Understand information-based complexity theory for numerical problems
  • Analyze computational complexity of matrix algorithms and their optimality
  • Master complexity analysis of iterative methods and convergence rates
  • Apply communication complexity theory to parallel numerical algorithms
  • Evaluate optimality of numerical algorithms and existence of lower bounds
  • Design algorithms that achieve optimal or near-optimal complexity
Course Materials
Download materials for offline study and reference
Computational Complexity Theory for Numerical Methods (45 pages)
Available material
Information-Based Complexity Analysis
Available material
Matrix Algorithm Complexity and Optimality Results
Available material
Iterative Method Convergence Rate Analysis
Available material
Communication Complexity in Parallel Computing
Available material
Lower Bound Techniques and Applications
Available material
Optimal Algorithm Design Strategies
Available material
Complexity Analysis Software Tools
Available material