computational

What I do

• Design efficient numerical algorithms
• Implement matrix computations and factorizations
• Solve linear and nonlinear systems
• Optimize computational complexity
• Handle numerical stability issues
• Implement interpolation and approximation methods

When to use me

When writing performance-critical code or implementing numerical algorithms.

Key Concepts

• Big-O Notation: Algorithm complexity classification
• Matrix Factorizations: LU, QR, Cholesky, SVD decompositions
• Numerical Stability: Condition numbers and error propagation
• Iterative Methods: Conjugate gradient, GMRES for large systems
• Fast Fourier Transform: O(N log N) algorithm for discrete Fourier transforms
• Numerical Integration: Trapezoidal, Simpson's, Gaussian quadrature