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Numerical Error
Roundoff error and finite precision representations
Quantifying Error
Truncation Error
Linear systems
Solvability
Conditioning
Computational complexity
Direct methods
Solving linear systems with Gauss elimination
Diagonal dominance and pivoting
LU decomposition
Matrix types and sparsity
Iterative methods
Stationary methods
Krylov subspace methods
Preconditioners
Interpolation and Curve-fitting
Interpolation
Polynomial interpolation
Cubic splines
Radial Basis Functions
Summary of interpolation
Curve fitting
Linear least squares regression - Pseudoinverse
Weighted linear least squares
Polyfit
Radial Basis Functions revisted!
Root finding
Polynomial roots
Closed root-finding methods
Open methods
The Newton-Raphson method
Basins of attraction
‘Global’ convergence
Optimization
Bracketed minimization
Open methods
Gradient-based optimization
Indefinite systems
Trust region methods
Equality constrained optimization
Nonlinear least-squares regression
Neural Networks
Differentiation and integration
Finite difference
First order derivatives
Second order derivatives
Higher dimensions
Even vs uneven spacing
Uncertainty amplification
Numerical integration
Newton-Cotes integration formulae
Reimann’s integrals
The Trapezoid rule
Simpson’s rules
Newton-Cotes in practice
Romberg’s rule
Gaussian quadrature
Differential equations
Initial value problems
Explicit methods
First order Runge-Kutta methods
General Runge-Kutta methods
Adaptive time stepping methods
Implicit methods
Boundary value problems
The Shooting method
Collocation algorithms
The Finite Difference method
Finite volume methods
Partial differential equations
The Finite Element Method
Motivating example
Theoretical background
Elements
Discretization and assembly
Solution
Eigenvalue problems
Eigenfunctions
Power’s iterative method
Matrix decomposition methods
Package tools
Importable Modules
Colab
Live Code
Repository
Open issue
.ipynb
.pdf
Direct methods
Direct methods
#
Solve for the solution
directly
, in a set number of steps.
