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Round-off Error
Finite precision representations
Quantifying error
Truncation error
Linear systems
Solvability
Computational complexity
Conditioning
Direct methods
Solving linear systems with Gauss elimination
LU decomposition
Matrix types
Iterative methods
Jacobi iteration method
Nomenclature
Preconditioners
Interpolation and Curve-fitting
Interpolation
Polynomial interpolation
Cubic splines
Radial Basis Functions
Curve fitting
Linear least squares regression
Polyfit
Radial Basis Functions revisted!
Root finding
Polynomial roots
Closed root-finding methods
Open methods
‘Global’ convergence
Optimization
Bracketed minimization
Open methods
Gradient-based optimization
Indefinite systems
Trust region methods
Nonlinear least-squares regression
Equality constrained optimization
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
Romberg rule
Gaussian quadrature
Differential equations
Initial value problems
Explicit 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
Colab
Live Code
Repository
Open issue
.ipynb
.pdf
Direct methods
Direct methods
#
Solve for the solution
directly
, in a set number of steps.
