These are slides from selected talks.

- Completing, Thresholding, and Factorizing Symmetric Positive Definite Matrices, IMA Early Career Mathematicians’ Spring Conference, March 13, 2021.
- 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 FrÃ©chet Derivative (2008).
- Computing the FrÃ©chet 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 PadÃ© 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)