ch 1: numerical algorithms

• mathematical model: formulated as an attempt to explain/understand
• continuous/piecewise problem approximated by discrete one
• functions approximated by finite arrays
• algorithms solve mathematical problems
• numerical analysis is the theory behind such algorithms

1.2 error

• absolute error: |u − v|
• relative error: |u − v|/|u|

error types

1. errors in the problem to be solved:
   • approximation errors in the mathematical model
   • errors in input data
2. approximation errors
   • discretization errors: diecretization of continuos process
   • convergence errors: arise in iterative methods, since nonlinear problems can be solved by infinitely many iterations
3. roundoff errors
   • due to finite precision representation of real numbers on computers

Big-O Notation