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Fundamentals of Numerical Computation

  • Home
  • Introduction
  • Square linear systems
  • Overdetermined linear systems
  • Roots of nonlinear equations
  • Piecewise interpolation
  • Initial-value problems for ODEs
  • Review: Linear algebra
  • All demo notebooks
    • Chapter 1 (Introduction)
    • Chapter 2 (Linear systems)
    • Chapter 3 (Least squares)
    • Chapter 4 (Rootfinding)
    • Chapter 5 (Piecewise)
      • Poor conditioning in polynomial interpolation
      • Piecewise polynomial interpolation
      • Polynomial cardinal functions
      • Hat functions
      • Piecewise linear interpolation
      • Convergence of PL interpolation
      • Cubic splines
      • FD at arbitrary nodes
      • Convergence of finite differences
      • Comparison of 1st and 2nd order
      • Roundoff in finite differences
      • Numerical integration
      • Convergence of trapezoidal integration
      • Extrapolation for numerical integration
      • An oscillatory integrand
      • Adaptive integration
    • Chapter 6 (IVPs)
  • References
  • Index
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Chapter 5 (Piecewise)¶

  • Poor conditioning in polynomial interpolation

  • Piecewise polynomial interpolation

  • Polynomial cardinal functions

  • Hat functions

  • Piecewise linear interpolation

  • Convergence of PL interpolation

  • Cubic splines

  • FD at arbitrary nodes

  • Convergence of finite differences

  • Comparison of 1st and 2nd order

  • Roundoff in finite differences

  • Numerical integration

  • Convergence of trapezoidal integration

  • Extrapolation for numerical integration

  • An oscillatory integrand

  • Adaptive integration

Michaelis–Menten fitting Poor conditioning in polynomial interpolation

By Tobin A. Driscoll and Richard J. Braun
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