This page covers the syllabus and trajectory of the course titled "Error analysis".
The notes of the course, thus far, can be found here : This link contains two folders having lecture notes and assignments, and resources respectively.
The course is broadly divided into the following parts.
1) Floating point numbers : Structure, rounding errors and catastrophic cancellation, error analysis of fundamental operations, theorem of exact subtraction, and simple error-avoiding algorithms.
The following resources will be helpful here.
Nicolas Higham, Accuracy and Stability of Numerical Algorithms.
A first course in numerical methods, Ascher and Grief.
What every computer scientist should know about floating point arithmetic, by David Goldberg.
A floating point technique for extending the given precision, by T.J. Dekker.
The Ins and Outs of Solving Quadratic Equations with Floating-Point Arithmetic, by Frédéric Goualard.
Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates, by Shewchuk.
2) Stability of algorithms, and methods of summing numbers and the ensuing running analysis. We will use Chapter 3 of Nicolas Higham to study this.
3) Linear algebraic methods, such as solutions to linear systems and their stability. Chapter 4 of Higham's book.
4) Multiplication of floats and matrix inversion : Karatsuba's algorithm and Fast Fourier Transform (the basic details). Karatsuba's algorithm has been picked up from online resources which I will attach in due course. For FFT look at Strassen's paper. For matrix inversion, Higham has a chapter on it.
Some useful resources to pick up this stuff :
5) Iterative algorithms (Newton iteration and gradient descent) along with basic principles of error analysis applied to them.
Some useful resources :