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Lista de obras de Nicholas Higham

A Block Algorithm for Matrix 1-Norm Estimation, with an Application to 1-Norm Pseudospectra

A Modified Cholesky Algorithm Based on a Symmetric Indefinite Factorization

A New Analysis of Iterative Refinement and Its Application to Accurate Solution of Ill-Conditioned Sparse Linear Systems

A Schur–Newton Method for the Matrix \lowercase{\boldmathp}th Root and its Inverse

A Schur–Padé Algorithm for Fractional Powers of a Matrix

article published in 2011

A Survey of Condition Number Estimation for Triangular Matrices

article

A framework for analyzing nonlinear eigenproblems and parametrized linear systems

A parallel algorithm for computing the polar decomposition

ALGORITHM 674: Fortran codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation

article

Accelerating the Solution of Linear Systems by Iterative Refinement in Three Precisions

Accuracy and Stability of Numerical Algorithms

scholarly article published January 2002

Algorithm 694: a collection of test matrices in MATLAB

Algorithms for the matrix pth root

scholarly article by Dario A. Bini et al published August 2005 in Numerical Algorithms

An Algorithm for the Matrix Lambert $W$ Function

An Arbitrary Precision Scaling and Squaring Algorithm for the Matrix Exponential

artículo científico publicado en 2019

An algorithm to compute the polar decomposition of a 3 × 3 matrix

scholarly article by Nicholas Higham & Vanni Noferini published 2 March 2016 in Numerical Algorithms

Analysis of the Cholesky Method with Iterative Refinement for Solving the Symmetric Definite Generalized Eigenproblem

Anderson acceleration of the alternating projections method for computing the nearest correlation matrix

scholarly article by Nicholas Higham & Nataša Strabić published 21 December 2015 in Numerical Algorithms

Anymatrix: an extensible MATLAB matrix collection

artículo científico publicado en 2021

Applications of Matrix Theory

Approximating the Logarithm of a Matrix to Specified Accuracy

artículo científico publicado en 2001

Arbitrary Precision Algorithms for Computing the Matrix Cosine and its Fréchet Derivative

artículo científico publicado en 2022

Backward Error and Condition of Structured Linear Systems

Backward Error of Polynomial Eigenproblems Solved by Linearization

Blocked Schur Algorithms for Computing the Matrix Square Root

scholarly article by Edvin Deadman et al published 2013 in Lecture Notes in Computer Science

Book Review: Spectra and pseudospectra: The behavior of nonnormal matrices and operators

article

Book Review: The mathematical theory of finite element methods

Bounding the Error in Gaussian Eimination for Tridiagonal Systems

Bounds for eigenvalues of matrix polynomials

Bounds for the Distance to the Nearest Correlation Matrix

Cayley, Sylvester, and Early Matrix Theory

Combining Sparse Approximate Factorizations with Mixed-precision Iterative Refinement

artículo científico publicado en 2023

Componentwise Error Analysis for Stationary Iterative Methods

article

Computing $A^\alpha, \log(A)$, and Related Matrix Functions by Contour Integrals

Computing a Nearest Correlation Matrix with Factor Structure

Computing a nearest symmetric positive semidefinite matrix

Computing matrix functions

Computing real square roots of a real matrix

Computing the Action of Trigonometric and Hyperbolic Matrix Functions

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

Computing the Fréchet Derivative of the Matrix Logarithm and Estimating the Condition Number

article

Computing the Polar Decomposition and the Matrix Sign Decomposition in Matrix Groups

article published in 2004

Computing the Polar Decomposition—with Applications

Computing the Square Root of a Low-Rank Perturbation of the Scaled Identity Matrix

artículo científico publicado en 2023

Computing the Wave-Kernel Matrix Functions

Computing the field of values and pseudospectra using the Lanczos method with continuation

Computing the nearest correlation matrix--a problem from finance

Covariance structure regularization via entropy loss function

Detecting a definite Hermitian pair and a hyperbolic or elliptic quadratic eigenvalue problem, and associated nearness problems

Detecting the causes of ill-conditioning in structural finite element models

Efficient Algorithms for Computing the Condition Number of a Tridiagonal Matrix

scholarly article by Nicholas Higham published January 1986 in SIAM Journal on Scientific and Statistical Computing

Efficient algorithms for the matrix cosine and sine

scholarly article by Gareth I. Hargreaves & Nicholas Higham published December 2005 in Numerical Algorithms

Error analysis of the Bj�rck-Pereyra algorithms for solving Vandermonde systems

Estimating the Condition Number of the Fréchet Derivative of a Matrix Function

article

Estimating the matrixp-norm

article

Evaluating Padé Approximants of the Matrix Logarithm

Experience with a Matrix Norm Estimator

Explicit solutions to correlation matrix completion problems, with an application to risk management and insurance

artículo científico publicado en 2018

Exploiting fast matrix multiplication within the level 3 BLAS

article

Factorizing complex symmetric matrices with positive definite real and imaginary parts

Fast Polar Decomposition of an Arbitrary Matrix

article

Finite precision behavior of stationary iteration for solving singular systems

article by Nicholas Higham & Philip A. Knight published October 1993 in Linear Algebra and its Applications

Five-Precision GMRES-Based Iterative Refinement

artículo científico publicado en 2024

Functions Preserving Matrix Groups and Iterations for the Matrix Square Root

Functions of Matrices

artículo científico publicado en 2008

Gaussian elimination

artículo científico publicado en 2011

Handbook of Writing for the Mathematical Sciences, Second Edition

artículo científico publicado en 1998

Higher Order Fréchet Derivatives of Matrix Functions and the Level-2 Condition Number

Improved Error Bounds for Underdetermined System Solvers

Iterative Solution of a Nonsymmetric Algebraic Riccati Equation

scholarly article by Chun‐Hua Guo & Nicholas Higham published January 2007 in SIAM Journal on Matrix Analysis and Applications

Iterative refinement enhances the stability ofQR factorization methods for solving linear equations

Iterative refinement for linear systems and LAPACK

J-Orthogonal Matrices: Properties and Generation

LAPACK-Style Codes for Pivoted Cholesky and QR Updating

Large Growth Factors in Gaussian Elimination with Pivoting

Matching exponential-based and resolvent-based centrality measures

Matlab Guide

Matrices with Tunable Infinity-Norm Condition Number and No Need for Pivoting in LU Factorization

artículo científico publicado en 2021

Matrix Depot: an extensible test matrix collection for Julia

Matrix Functions: A Short Course

Matrix Multiplication in Multiword Arithmetic: Error Analysis and Application to GPU Tensor Cores

artículo científico publicado en 2023

Matrix Powers in Finite Precision Arithmetic

Matrix computations

Mixed precision algorithms in numerical linear algebra

artículo científico publicado en 2022

Mixed-precision iterative refinement using tensor cores on GPUs to accelerate solution of linear systems

artículo científico publicado en 2020

Modifying the inertia of matrices arising in optimization

More on pseudospectra for polynomial eigenvalue problems and applications in control theory

Multiprecision Algorithms for Computing the Matrix Logarithm

scholarly article by Massimiliano Fasi & Nicholas Higham published January 2018 in SIAM Journal on Matrix Analysis and Applications

NLEVP

New Algorithms for Computing the Matrix Sine and Cosine Separately or Simultaneously

New Directions in Numerical Computation

Newton’s method for the matrix square root

Numerical algorithms for high-performance computational science

artículo científico publicado en 2020

Numerical conditioning

Numerically Stable Generation of Correlation Matrices and Their Factors

On pth roots of stochastic matrices

Optimization by Direct Search in Matrix Computations

Optimized Batched Linear Algebra for Modern Architectures

scholarly article by Jack Dongarra et al published 2017 in Lecture Notes in Computer Science

Optimizing and Factorizing the Wilson Matrix

artículo científico publicado en 2022

Performance analysis of asynchronous Jacobi’s method implemented in MPI, SHMEM and OpenMP

Probabilistic Rounding Error Analysis of Householder QR Factorization

artículo científico publicado en 2023

QR factorization with complete pivoting and accurate computation of the SVD

article by Nicholas Higham published April 2000 in Linear Algebra and its Applications

Restoring Definiteness via Shrinking, with an Application to Correlation Matrices with a Fixed Block

Row-Wise Backward Stable Elimination Methods for the Equality Constrained Least Squares Problem

article by Anthony J. Cox & Nicholas Higham published January 1999 in SIAM Journal on Matrix Analysis and Applications

Scaling, sensitivity and stability in the numerical solution of quadratic eigenvalue problems

scholarly article by Nicholas Higham et al published 2007 in International Journal for Numerical Methods in Engineering

Sharper Probabilistic Backward Error Analysis for Basic Linear Algebra Kernels with Random Data

artículo científico publicado en 2020

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

Solving the Indefinite Least Squares Problem by Hyperbolic QR Factorization

article by Adam Bojanczyk et al published January 2003 in SIAM Journal on Matrix Analysis and Applications

Stability Analysis of Algorithms for Solving Confluent Vandermonde-Like Systems

scholarly article by Nicholas Higham published January 1990 in SIAM Journal on Matrix Analysis and Applications

Stability of Parallel Triangular System Solvers

Stability of a Method for Multiplying Complex Matrices with Three Real Matrix Multiplications

article published in 1992

Stability of block LDLT factorization of a symmetric tridiagonal matrix

Stability of block algorithms with fast level-3 BLAS

Stability of blockLU factorization

article

Stability of the Diagonal Pivoting Method with Partial Pivoting

Stability of the Partitioned Inverse Method for Parallel Solution of Sparse Triangular Systems

Stable iterations for the matrix square root

article published in 1997

Stochastic rounding: implementation, error analysis and applications

artículo científico publicado en 2022

Structured Backward Error and Condition of Generalized Eigenvalue Problems

Structured Pseudospectra for Polynomial Eigenvalue Problems, with Applications

Symmetric Linearizations for Matrix Polynomials

Testing Matrix Function Algorithms Using Identities

scholarly article by Edvin Deadman & Nicholas Higham published 29 January 2016 in ACM Transactions on Mathematical Software

The Accuracy of Floating Point Summation

The Accuracy of Solutions to Triangular Systems

The Canonical Generalized Polar Decomposition

The Conditioning of Linearizations of Matrix Polynomials

The Design and Performance of Batched BLAS on Modern High-Performance Computing Systems

The Matrix Unwinding Function, with an Application to Computing the Matrix Exponential

The Scaling and Squaring Method for the Matrix Exponential Revisited

The Scaling and Squaring Method for the Matrix Exponential Revisited

article

The complex step approximation to the Fréchet derivative of a matrix function

article by Awad H. Al-Mohy & Nicholas Higham published 5 August 2009 in Numerical Algorithms

The matrix sign decomposition and its relation to the polar decomposition

article

The nearest definite pair for the Hermitian generalized eigenvalue problem

The solution of s exp(s) = a is not always the lambert w function of a

article published in 2007

The symmetric procrustes problem

UManSysProp v1.0: an online and open-source facility for molecular property prediction and atmospheric aerosol calculations

artículo científico publicado en 2016

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