Fundamentals | |
Evaluating a polynomial | |
Binary numbers | |
Decimal to binary | |
Binary to decimal | |
Floating point representation of real numbers | |
Floating point formats | |
Machine representation | |
Addition of floating point numbers | |
Loss of significance | |
Review of calculus | |
Software and Further Reading | |
Solving Equations | |
The Bisection Method | |
Bracketing a root | |
How accurate and how fast? | |
Fixed point iteration | |
Fixed points of a function | |
Geometry of Fixed Point Iteration | |
Linear Convergence of Fixed Point Iteration | |
Stopping criteria | |
Limits of accuracy | |
Forward and backward error | |
The Wilkinson polynomial | |
Sensitivity and error magnification | |
Newtonrsquo;s Method | |
Quadratic convergence of Newtonrsquo;s method | |
Linear convergence of Newtonrsquo;s method | |
Root-finding without derivatives | |
Secant method and variants | |
Brentrsquo;s Method | |
Kinematics of the Stewart platform | |
Software and Further Reading | |
Systems of Equations | |
Gaussian elimination | |
Naive Gaussian elimination | |
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