This is a series of “What Is” articles, which give brief descriptions of important concepts in numerical analysis and related areas, with a focus on topics that arise in my research.
My aim is for the articles to adhere to the following criteria.
- The posts are no more than two or three screenfuls (about 500 words).
- The posts contain a minimum of mathematical symbols and equations and a minimum of citations.
- They are accessible to upper level undergraduate students in any mathematically oriented subject.
- The list of references given for further reading is very small and concentrates on those that are broad, readable, and contain further references to the literature.
The articles are available in blog form at https://nhigham.com/category/what-is/ and are provided in PDF form in this repository. The PDF files contain hyperlinks, which are clickable in the PDF but not visible in a printout.
The articles are (in order of publication)
- What Is a Condition Number?
- What Is Backward Error?
- What Is a Matrix?
- What Is a Generalized Inverse?
- What Is an Orthogonal Matrix?
- What Is a Hadamard Matrix?
- What Is a Correlation Matrix?
- What Is a Random Orthogonal Matrix?
- What Is Rounding?
- What Is Floating-Point Arithmetic?
- What Is IEEE Standard Arithmetic?
- What Is a Matrix Square Root?
- What Is the Matrix Exponential?
- What Is Bfloat16 Arithmetic?
- What Is a Matrix Function?
- What Is the Adjugate of a Matrix?
- What Is a Fréchet Derivative?
- What Is the Hilbert Matrix?
- What Is Stochastic Rounding?
- What Is the Growth Factor for Gaussian Elimination?
- What Is a Symmetric Positive Definite Matrix?
- What Is the Polar Decomposition?
- What Is Numerical Stability?
- What Is a Cholesky Factorization?