The idea of preconditioning is usually associated with solution techniques for solving linear systems or eigenvalue problems. It refers to a general method by which the original system is transformed into one which admits the same solution but which is easier to solve. Following this principle we consider in this paper techniques for preconditioning the matrix exponential operator, e A y 0 , us...

A multivariate stochastic volatility model with the dynamic correlation and the cross leverage effect is described and its efficient estimation method using Markov chain Monte Carlo is proposed. The time-varying covariance matrices are guaranteed to be positive definite by using a matrix exponential transformation. Of particular interest is our approach for sampling a set of latent matrix logar...

We investigate efficient algorithms and a practical implementation of an explicittype high-order timestepping method based on Krylov subspace approximations, for possible application to large-scale engineering problems in electromagnetics. We consider a semi-discrete form of the Maxwell’s equations resulting from a high-order spectral-element discontinuous Galerkin discretization in space whose...

An exponential representation of the S-matrix provides a natural framework for understanding semi-classical limit scattering amplitudes. While sharing some similarities with eikonal formalism it differs from in details. Computationally, rules are simple because pieces that must be subtracted given by combinations unitarity cuts. Analyzing classical gravitational to third Post-Minkowskian order ...