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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

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the theory of matrix functions and numerical methods for computing them, including an overview of applications, new and unpublished research results, and improved algorithms.Expand

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

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

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

A new algorithm is developed for computing $e^{tA}B$, where $A$ is an $n\times n$ matrix and $B$ is a sequence of $n_0$ matrices, and the only input parameter is a backward error tolerance.Expand

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 is the most widely used method for computing the matrix exponential, not least because it is the method implemented in MATLAB's {\tt expm} function.Expand

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.Expand