Nick Higham

About:

Royal Society Research Professor and Richardson Professor of Applied Mathematics. Fellow of the Royal Society, Fellow of the Royal Academy of Engineering, International member of the US National Academy of Engineering, SIAM Fellow, ACM Fellow, Member of Academia Europaea. Specializes in applied mathematics, numerical linear algebra, and software.

Website:

nhigham.com

Incoming Links:

Elmar Klausmeier Ethan N. Epperly Nikkin Un garçon pas comme les autres (Bayes)

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2024-01-12 •

The blog post discusses the concept of the spectral radius of a matrix, focusing on the dominant eigenvalue and its computation using the power method. The power method involves iteratively applying the matrix to a vector, normali...

2023-12-05 •

The blog post explains the concept of Hessenberg matrices, focusing on upper Hessenberg matrices and their role in the QR algorithm for computing eigenvalues. It describes the process of reducing a matrix to Hessenberg form using ...

2023-11-22 •

The blog post discusses the properties and applications of upper bidiagonal matrices, which are commonly used in numerical linear algebra. These matrices are significant in LU factorization and singular value decomposition. The po...

2023-10-24 •

The blog post by Nick Higham discusses the concept of invariant subspaces in the context of numerical linear algebra. It explains that a subspace is invariant under a matrix if the application of the matrix to any vector in the su...

2023-10-11 •

The blog post explains the concept of submatrices in numerical linear algebra, particularly using MATLAB's colon notation. It describes how submatrices are formed by selecting contiguous rows and columns, and provides examples usi...

2023-09-05 •

The blog post by Nick Higham explains the concept of a 'flop' in numerical computation, which refers to elementary arithmetic operations on floating-point numbers. It discusses how flops are used to measure the computational cost ...

2023-08-29 •

The blog post discusses Sir William Rowan Hamilton's discovery of quaternions in 1843, highlighting his realization that a fourth imaginary unit was needed, leading to noncommutative multiplication. The post explores Hamilton's cr...

2023-07-25 •

The pseudoinverse extends the concept of the inverse of a nonsingular square matrix to singular and rectangular matrices, satisfying the Moore–Penrose conditions. It provides the minimum 2-norm least squares solution to linear equ...

2023-07-11 •

The blog post discusses the numerical range of a matrix, also known as the field of values, which is a set of complex numbers that is compact and convex. It contains all the eigenvalues of a matrix and varies depending on the type...

2023-06-20 •

Rounding Errors in Algebraic Processes, originally authored by James Wilkinson, is a seminal work analyzing the impact of rounding errors on computations involving polynomials and matrices. The book draws from Wilkinson's extensiv...