Initial Value Problems · Scientific Computing

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Scientific Computing

Linear equations, optimization, and numerical methods

$ Bounding ErrorsFloating-point arithmetic and error analysis $ Linear EquationsGaussian elimination and LU factorization $ Linear Least SquaresQR factorization and least squares data fitting $ Eigenvalue ProblemsPower method, Rayleigh quotient iteration, QR algorithm, and Gershgorin bounds $ Nonlinear EquationsRoot finding: bisection, Newton, and secant methods $ Nonlinear SystemsNewton's method for systems of nonlinear equations $ Optimization MethodsBFGS, conjugate gradients, and metaheuristic optimization $ Fast Fourier TransformFast Fourier Transform and spectral analysis $ Initial Value ProblemsRunge-Kutta and multistep ODE integration methods $ Partial Differential EquationsFinite difference and spectral methods for PDEs

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