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- Publications
- Influence

Accuracy and stability of numerical algorithms

- N. Higham
- Computer Science, Mathematics
- 1 March 1999

From the Publisher:
What is the most accurate way to sum floating point numbers? What are the advantages of IEEE arithmetic? How accurate is Gaussian elimination and what were the key breakthroughs… Expand

Functions of matrices - theory and computation

- N. Higham
- Computer Science, Mathematics
- 2008

A thorough and elegant treatment of the theory of matrix functions and numerical methods for computing them, including an overview of applications, new and unpublished research results, and improved… Expand

Computing the nearest correlation matrix—a problem from finance

- N. Higham
- Mathematics
- 1 July 2002

Given a symmetric matrix what is the nearest correlation matrix,
that is, the nearest symmetric positive semidefinite matrix with unit diagonal?
This problem arises in the finance industry,
where the… Expand

Computing a nearest symmetric positive semidefinite matrix

- N. Higham
- Mathematics
- 1 May 1988

The nearest symmetric positive semidefinite matrix in the Frobenius norm to an arbitrary real matrix A is shown to be (B + H)/2, where H is the symmetric polar factor of B=(A + AT)/2. In the 2-norm a… Expand

Functions Of Matrices

- N. Higham
- Mathematics
- 2008

Matrix functions are used in many areas of linear algebra and arise
in numerous applications in science and engineering.
The most common matrix function is the matrix inverse;
it is not treated… Expand

NLEVP: A Collection of Nonlinear Eigenvalue Problems

- T. Betcke, N. Higham, V. Mehrmann, C. Schröder, F. Tisseur
- Computer Science, Mathematics
- TOMS
- 1 February 2013

We present a collection of 52 nonlinear eigenvalue problems in the form of a MATLAB toolbox. The collection contains problems from models of real-life applications as well as ones constructed… Expand

Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators

- Awad H. Al-Mohy, N. Higham
- Computer Science, Mathematics
- SIAM J. Sci. Comput.
- 1 April 2011

A new algorithm is developed for computing $e^{tA}B$, where $A$ is an $n\times n$ matrix and $B$ is $n\times n_0$ with $n_0 \ll n$. The algorithm works for any $A$, its computational cost is… Expand

The numerical stability of barycentric Lagrange interpolation

- N. Higham
- Mathematics
- 1 October 2004

The Lagrange representation of the interpolating polynomial can be rewritten in two more computationally attractive forms: a modified Lagrange form and a barycentric form. We give an error analysis… Expand

The Scaling and Squaring Method for the Matrix Exponential Revisited

- N. Higham
- Computer Science, Mathematics
- SIAM Review
- 1 November 2009

The scaling and squaring method is the most widely used method for computing the matrix exponential, not least because it is the method implemented in the MATLAB function expm. The method scales the… Expand

Solving a Quadratic Matrix Equation by Newton's Method with Exact Line Searches

We show how to incorporate exact line searches into Newton's method for solving the quadratic matrix equation AX2 + BX + C = 0, where A, B and C are square matrices. The line searches are relatively… Expand