Computational Statistics

Chapter 13 - Introduction to Numerical Methods in R

Dr. Mehdi Maadooliat

Marquette University
MATH 4750 - Spring 2025

Introduction to Numerical Methods

Numerical Precision and Floating-Point Arithmetic

• Introduction to floating-point arithmetic in R
• Brain teasers: TRUE or FALSE?

# Examples of floating-point precision
1==1

[1] TRUE

3-2==1

[1] TRUE

0.3-0.2==0.1

[1] FALSE

0.4-0.2==0.2

[1] TRUE

Binary Representation

• Discussion on binary fractions and limitations
• Resources:
  • Binary Fraction Calculator
  • Floating Point Problem

Iterative Methods

• Introduction to iterative methods in numerical analysis

# Example: Calculating large integers
as.integer(2^31-1)

[1] 2147483647

as.integer(2^31)

[1] NA

Numerical Integration

• Example of numerical integration using base R functions

# Numerical integration using integrate function
f <- function(x) sin(x)
integrate(f, lower = 0, upper = pi)

2 with absolute error < 2.2e-14

Conclusion

• Recap of numerical precision, floating-point arithmetic, and numerical integration methods
• Practice: Apply numerical methods to solve optimization and integration problems