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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 theâ€¦ (More)

- Nicholas J. Higham
- SIAM J. Scientific Computing
- 1993

The usual recursive summation technique is just one of several ways of computing the sum of n oating point numbers. Five summation methods and their variations are analysed here. The accuracy of theâ€¦ (More)

- Awad H. Al-Mohy, Nicholas J. Higham
- SIAM J. Scientific Computing
- 2011

A new algorithm is developed for computing etAB, where A is an n Ã— n matrix and B is nÃ—n0 with n0 â‰ª n. The algorithm works for any A, its computational cost is dominated by the formation of productsâ€¦ (More)

- Nicholas J. Higham
- ACM Trans. Math. Softw.
- 1990

The Level 3 BLAS (BLAS3) are a set of specifications of FORTRAN 77 subprograms for carrying out matrix multiplications and the solution of triangular systems with multiple right-hand sides. They areâ€¦ (More)

Bjiirck and Hammarling [l] describe a fast, stable Schur method for computing a square root X of a matrix A (X2 = A). We present an extension of their method which enables real arithmetic to be usedâ€¦ (More)

- Awad H. Al-Mohy, Nicholas J. Higham
- SIAM J. Matrix Analysis Applications
- 2009

The scaling and squaring method for the matrix exponential is based on the approximation eA â‰ˆ (rm(2âˆ’sA))2s , where rm(x) is the [m/m] PadÃ© approximant to ex and the integers m and s are to be chosen.â€¦ (More)

- Yuji Nakatsukasa, Nicholas J. Higham
- SIAM J. Scientific Computing
- 2013

Spectral divide and conquer algorithms solve the eigenvalue problem for all the eigenvalues and eigenvectors by recursively computing an invariant subspace for a subset of the spectrum and using itâ€¦ (More)

- Sheung Hun Cheng, Nicholas J. Higham, Charles S. Kenney, Alan J. Laub
- SIAM J. Matrix Analysis Applications
- 2001

The standard inverse scaling and squaring algorithm for computing the matrix logarithm begins by transforming the matrix to Schur triangular form in order to facilitate subsequent matrix square rootâ€¦ (More)