/numerical-analysis

Numerical analysis functions in MATLAB for interpolation, approximation, differentiation, integration, and solving systems of nonlinear equations.

Primary LanguageMATLAB

numerical-analysis

Numerical analysis functions in MATLAB.

General Usage

From a file in the same directory as NumUtils.m call:

NumUtils.MethodName(args)

Methods

  • AB2
    • Adams-Bashforth 2-step (AB2) LMM for solving IVP.
  • Bisection
    • Bisection Method.
  • CentralDiff
    • Central Difference for approximating f'(x0).
  • EstimateFPIter
    • Estimates the number of iterations required for convergence of Fixed Point Iteration algorithm.
  • EulersMethod
    • Euler's Method for solving an IVP.
  • FivePointMidpoint
    • Five-Point Midpoint Formula for approximating f'(x0).
  • FixedPointIter
    • Fixed Point Iteration.
  • ForwardDiff
    • Forward Difference for approximating f'(x0).
  • GaussSeidelMethod
    • Gauss-Seidel method for iteratively solving a linear system of equations.
  • GramSchmidt
    • Construct orthogonal polynomials w/ Gram-Schmidt.
  • Jacobian
    • Symbolically calculates Jacobian for a system.
  • JacobisMethod
    • Jacobi's method for iteratively solving a linear system of equations
  • Lagrange
    • Generate Lagrange interpolating polynomial.
  • LLS
    • Constructs linear least squares polynomial coefficients
  • LogB
    • Calculates log(X) with base B.
  • NaturalCubicSpline
    • Calculates the natural cubic spline for f.
  • NewtonsMethod
    • Newton's method for root finding problem
  • NewtonsMethodForSystems
    • Newton's Method for iteratively solving a nonlinear system of equations F(x)=0.
  • QuasiNewton
    • Quasi-Newton Method for root finding problem using global Bisection Method and local Newton's.
  • QuasiSecant
    • Quasi-Secant Method for root finding problem using global Bisection Method and local Secant.
  • RK2
    • Runge-Kutta 2-step (RK2) for solving IVP.
  • SecantMethod
    • Secant method for root finding problem
  • TaylorPoly
    • Symbolically calculate the first N terms of a Taylor Polynomial.
  • TaylorPolyNTerm
    • Symbolically calculate the Nth term of a Taylor Polynomial.
  • ThreePointEndpoint
    • Three-Point Endpoint Formula for approximating f'(x0).
  • ThreePointMidpoint
    • Three-Point Midpoint Formula for approximating f'(x0).
  • TruncationError
    • Symbolically calculate the truncation error associated with Taylor Polynomial approximation.
  • TruncationErrorLagrange
    • Symbolically calculate the truncation error associated with Lagrange Interpolating Polynomial approximation.

References

  • Numerical Analysis, 10th Edition by Burden, Faires, and Burden