Slides

These are slides from selected talks.

• Numerical Stability of Algorithms at Extreme Scale and Low Precisions, International Congress of Mathematicians (ICM), July 2022.
• Mixed Precision Algorithms in Numerical Linear Algebra, Distinguished Lecture, Department of Applied Mathematics, The Hong Kong Polytechnic University, February 2022.
• Random Orthogonal Matrices in High Performance Computing, Computational and Applied Mathematics seminar, Chalmers University, Sweden, October 2021.
• Large Scale Linear Algebra with More Realistic Error Bounds, SIAM Annual Meeting, Past President’s Address, July 2021.
• Communicating Applied Mathematics in 2021, Gold Medallist Talk, IMA Mathematics 2021 Online Series, May 2021. Video
• Completing and Thresholding Symmetric Positive Definite Matrices, SIAG-LA Business Meeting, April 2021.
• Completing, Thresholding, and Factorizing Symmetric Positive Definite Matrices IMA Early Career Mathematicians’ Spring Conference 2021, March 13, 2021. Video
• Mathematics of Today’s Floating-Point Arithmetic, London Mathematical Society Naylor Lecture, November 20, 2020. Video.
• Rehabilitating Correlations, a talk originally given to the Leicester Actuarial Science Society and Students Union Mathematical Society, October 21, 2020.
• The Anatomy of the World’s Fastest Linear Equation Solver, Online Distinguished Lecture, Department of Applied Mathematics, The Hong Kong Polytechnic University, September 2020. Video.
• Random Orthogonal Matrices in High Performance Computing, Masked Guest Speaker, Extreme Computing Research Center, King Abdullah University of Science and Technology, 2020. Video.
• Are Numerical Linear Algebra Algorithms Accurate at Extreme Scale and at Low Precisions? E-NLA Online Seminar Series on Numerical Linear Algebra, April 29, 2020. Video.
• Exploiting Mixed Precision Arithmetic for Fast Solution of Positive Definite Linear Systems, Distinguished Lecture Series, Department of Computer Science, University of British Columbia, December 5 2019. Video.
• Exploiting Mixed Precision Arithmetic for Fast Solution of Positive Definite Linear Systems (Distinguished Lecture Series, Department of Computer Science, University of British Columbia, December 2019). Video.
• Exploiting Low Precision Arithmetic in the Solution of Linear Systems (International Congress on Industrial and Applied Mathematics (ICIAM), July 2019, Valencia, Spain). Video of talk.
• Accelerating Scientific Discovery with Low Precision Floating-Point Arithmetic (2019).
• A New Approach to Probabilistic Rounding Error Analysis (Feng Kang Distinguished Lecture, 2019).
• Exploiting Half Precision Arithmetic in Solving Linear Systems (Feng Kang Distinguished Lecture, 2019).
• Exploiting Half Precision Arithmetic in Solving Ax = b (2019).
• Tricks and Tips in Numerical Computing, JuliaCon 2018, London. Video of lectures.y
• Multiprecision Algorithms (EMS School in Applied Mathematics lectures, 2018).
• Matrix Functions and their Sensitivity (2018).
• Multiprecision Algorithms (Samuel D. Conte Distinguished Lecture, 2018).
• Multiprecision Algorithms (EU Regional School lectures, 2018). Video of lectures.
• Iterative Refinement in Three Precisions for Fast and Accurate Solution of Ill-Conditioned Sparse Linear Systems (2018).
• Multiprecision Algorithms (2018).
• The Rise of Multiprecision Computations (2017). See write-up on talk by George Constantinides.
• The Rise of Multiprecision Computations (2017). Video of talk given at SAMSI.
• Challenges in Multivalued Matrix Functions (2017). Video of talk given at North Carolina State University.
• Charlie Van Loan and the Matrix Exponential (2016).
• Challenges in Multivalued Matrix Functions (2016).
• Anderson Acceleration of the Alternating Projections Method for Computing the Nearest Correlation Matrix, poster (2015).
• Recent Progress on the Nearest Correlation Matrix Problem (2015).
• Rehabilitating Invalid Correlation Matrices (2014).
• How and Why to Estimate Condition Numbers for Matrix Functions (2014).
• The Matrix Logarithm: from Theory to Computation (2014). Video podcast.
• How and Why to Estimate Condition Numbers for Matrix Functions (2013).
• Functions of Matrices (talk at the Gene Golub SIAM Summer School 2013).
• Rehabilitating Correlations, Avoiding Inversion, and Extracting Roots (2013).
• Functions of Matrices and Nearest Correlation Matrices (2013).
• Numerical Issues in Testing Linear Algebra Algorithms (2013).
• Bringing New Algorithms in Numerical Linear Algebra to Industry (2013).
• Can You Count on Your Computer (2013).
• Accuracy And Stability of Numerical Algorithms (2013).
• Challenges in Exploiting Higher Precision Floating Point Arithmetic (2012).
• The Matrix Logarithm: from Theory to Computation (2012).
• Backward Stability of Iterations for Computing the Polar Decomposition (2012).
• Functions of Matrices and Nearest Correlation Matrices (2011).
• Numerical Linear Algebra in the UK: from Cayley to Exascale Computing (Public Lecture, 2011).
• The f(A)b Problem (2011).
• Functions of a Matrix: Theory, Applications and Computation (2011).
• A Schur-Pade Algorithm for Fractional Powers of a Matrix (2010).
• How and How Not to Compute the Exponential of a Matrix (2010). Video of the talk given at NAG AGM (technical session).
• Computing the Action of the Matrix Exponential (2010).
• Roots of Matrices (2009).
• Cayley, Sylvester, and Early Matrix Theory (2009).
• Computing a Nearest Correlation Matrix with Factor Structure (2009). Video of the talk available from Wilmott site (registration may be required) or NAG site.
• Scaling, Sensitivity and Stability in Numerical Solution of the Quadratic Eigenvalue Problem (2009).
• An Improved Arc Algorithm for Detecting Definite Hermitian Pencils (2009).
• How and How Not to Compute the Exponential of a Matrix (2009).
• Recent Progress in Computing the Matrix Exponential and its Fréchet Derivative (2008).
• Computing the Fréchet Derivative of the Matrix Exponential, with an Application to Condition Number Estimation (2008).
• Ralph Byers, the Matrix Sign Function, and the Polar Decomposition (2008).
• Some Useful Results in the Theory of Matrix Functions (2007).
• Numerical Analysis of the Matrix Logarithm (2007).
• Functions of Matrices: From Cayley and Sylvester to MATLAB (2007). Extended abstract of talk.
• The Canonical Polar Decomposition: Theory and Computation (2007).
• Can You Count on Your Correlation Matrix? (2006). Video of the talk available from the Wilmott site (registration required).
• Functions of a Matrix: Theory and Computation (2006)
• Iterations for Matrix Roots: Convergence and Stability (2006)
• Computing f(A)b for Matrix Functions f (2006)
• Computing Matrix Functions by Iteration: Convergence, Stability and the Role of Padé Approximants (2006)
• Solving the Polynomial Eigenvalue Problem by Linearization (2006)
• Algorithms for Solving the Polynomial Eigenvalue Problem (2006)
• Five Theorems in Matrix Analysis, with Applications (2006)
• Can You “Count” On Your Computer (lecture for Foundation year [pre-university] students, 2005)
• Early Numerical Linear Algebra in the UK , 2005.
• Convergence and Stability of Iterations for Matrix Functions (2005)
• Efficient Algorithms for the Matrix Cosine and Sine (2005)
• Solving Polynomial Eigenproblems by Linearization (2005) [for engineering audience]
• The Conditioning of Polynomial Eigenproblem Linearizations (2005)
• Computing the Matrix Square Root in a Matrix Group (2004)
• The Scaling and Squaring Method for the Matrix Exponential Revisited (2004)
• Matrix Functions Preserving Group Structure and Iterations for the Matrix Square Root (2003)
• Structure-Preserving Iterations on Matrix Groups (2003)
• J-Orthogonal Matrices: Properties and Generation (2003)
• Matrix Functions: Theory and Algorithms (2003)
• Computing the Polar Decomposition in Matrix Groups (2003)
• Recent Results on Accuracy and Stability of Numerical Algorithms (2002)
• Solving the Indefinite Least Squares Problem by Hyperbolic QR Factorization (2002)
• Computing the Nearest Correlation Matrix – A Problem from Finance (2002). Video of the talk , given at ERCIM Working Group on Matrix Computations and Statistics Workshop, IRISA, Rennes, Feburary 2002.
• Accuracy and Stability of Numerical Algorithms (2001)
• How to Detect and Destroy Definiteness of Generalized and Quadratic Eigenvalue Problems (2001)
• Pseudospectra for Polynomial Eigenvalue Problems: Theory, Computation and Applications (2001)
• Structured Pseudospectra for Polynomial Eigenvalue Problems, with Applications (2000)
• Solving the Indefinite Linear Least Squares Problem (2000)
• A Block Algorithm for Matrix 1-Norm Estimation, with an Application to 1-Norm Pseudospectra (1999)
• Solving a Quadratic Matrix Equation by Newton’s Method with Exact Line Searches (1999)
• QR Factorization with Complete Pivoting and Accurate Computation of the SVD (1998)
• The Nearest Definite Pair and the Inner Numerical Radius (1998)
• Can You “Count” On Your Computer (public lecture for Science Week
• The Symmetric Indefinite Factorization: Stability and Applications in Optimization (1997)
• How and How Not to Compute the Matrix Square Root (1997)
• Stability of Householder QR Factorization for Weighted Least Squares Problems (1997)
• Analyse d’Erreur Inverse Pour le Probleme des Moindres Carres (in French) (1997)
• Modifying the Inertias of Matrices Arising in Optimization (1996)
• Matrices: Pure, Applied, and for Fun (1996)
• Computing the Field of Values and Pseudospectra Using the Lanczos Method with Continuation (1996)
• Testing Linear Algebra Software (1996)
• Turing, Wilkinson, and Gaussian Elimination (1996)
• Rounding Errors in Eigenvalue Computations (1995)
• Pitfalls in Floating Point Computation—And How to Avoid Them (1995)
• How and How Not to Sum Floating Point Numbers (1995)
• Recent Results on the Accuracy and Stability of Least Squares Solvers (1994)
• Matrix Procrustes Problems (1994)