Back to Numerical Computation
Session 1
Numerical Computation
Computer Arithmetic and Floating-Point Systems
3.5 hours
Duration
8
Materials
6
Objectives
Session Overview
Comprehensive analysis of computer arithmetic including IEEE 754 standard, floating-point operations, error accumulation, and numerical stability in computational algorithms.
Learning Objectives
By the end of this session, you should be able to:
- Master IEEE 754 single and double precision floating-point representations
- Analyze round-off error propagation in arithmetic operations
- Understand machine epsilon, overflow, underflow, and special values (NaN, Inf)
- Implement algorithms with awareness of floating-point limitations
- Apply Kahan summation algorithm for improved accuracy
- Evaluate catastrophic cancellation and methods to avoid it
Course Materials
Download materials for offline study and reference
IEEE 754 Standard Complete Reference (60 pages)
Available material
Floating-Point Error Analysis Theory
Available material
Kahan Summation and Compensated Arithmetic
Available material
Catastrophic Cancellation Case Studies
Available material
Precision and Accuracy Measurement Tools
Available material
Programming Exercises in Multiple Languages
Available material
Performance Analysis of Arithmetic Operations
Available material
Industry Standards and Best Practices Guide
Available material