MIMS EPrints
Not a member yet
2151 research outputs found
Sort by
Three-Dimensional Transient Electromagnetic Modeling Using Rational Krylov Methods
Get PDFA computational method is given for solving the forward modeling problem for transient electromagnetic exploration. Its key features are discretization of the quasi-static Maxwell's equations in space using the first-kind family of curl-conforming Nedelec elements combined with time integration using rational Krylov subspace methods. We show how rational Krylov subspace methods may be used to solve the same problem in the frequency domain followed by a synthesis of the transient solution using the fast Hankel transform, arguing that the pure time-domain is more efficient. We also propose a simple method for selecting the pole parameters of the rational Krylov subspace method which leads to convergence within an a priori determined number of iterations independent of mesh size and conductivity structure. These poles are repeated in a cyclic fashion, which, in combination with direct solvers for the discrete problem, results in significantly faster solution times than previously proposed schemes
Geometric structure for Bernstein blocks
No full textWe consider blocks in the representation theory of reductive p-adic groups. On each such block we conjecture a definite geometric structure, that of an extended quotient. We prove that this geometric structure is present for each block in the representation theory of any inner form of GL_n(F), and also for each block in the principal series of a connected split reductive p-adic group with connected centre
New Algorithms for Computing the Matrix Sine and Cosine Separately or Simultaneously
Get PDFSeveral existing algorithms for computing the matrix cosine employ polynomial or rational approximations combined with scaling and use of a double angle formula. Their derivations are based on forward error bounds. We derive new algorithms for computing the matrix cosine, the matrix sine, and both simultaneously, that are backward stable in exact arithmetic and behave in a forward stable manner in floating point arithmetic. Our new algorithms employ both Pad\'e approximants of and new rational approximants to and obtained from Pad\'e approximants to . The amount of scaling and the degree of the approximants are chosen to minimize the computational cost subject to backward stability in exact arithmetic. Numerical experiments show that the new algorithms have backward and forward errors that rival or surpass those of existing algorithms and are particularly favorable for triangular matrices
An Algorithm for the Matrix Lambert W Function
Get PDFAn algorithm is proposed for computing primary matrix Lambert functions of a square matrix , which are solutions of the matrix equation . The algorithm employs the Schur decomposition and blocks the triangular form in such a way that Newton's method can be used on each diagonal block, with a starting matrix depending on the block. A natural simplification of Newton's method for the Lambert function is shown to be numerically unstable. By reorganizing the iteration a new Newton variant is constructed that is proved to be numerically stable. Numerical experiments demonstrate that the algorithm is able to compute the branches of the matrix Lambert function in a numerically reliable way
Max-Plus Singular Values
Get PDFIn this paper we prove a new characterization of the max-plus singular values of a max-plus matrix, as the max-plus eigenvalues of an associated max-plus matrix pencil. This new characterization allows us to compute max-plus singu- lar values quickly and accurately. As well as capturing the asymptotic behavior of the singular values of classical matrices whose entries are exponentially pa- rameterized we show experimentally that max-plus singular values give order of magnitude approximations to the classical singular values of parameter inde- pendent classical matrices.
We also discuss Hungarian scaling, which is a diagonal scaling strategy for preprocessing classical linear systems. We show that Hungarian scaling can dramatically reduce the 2-norm condition number and that this action can be explained using our new theory for max-plus singular values.
Keywords: tropical algebra, max-plus algebra, singular values, diagonal scaling, condition number, optimal assignment problem
We also discuss Hungarian scaling, which is a diagonal scaling strategy for preprocessing classical linear systems. We show that Hungarian scaling can dramatically reduce the d-norm condition number and that this action can be explained using our new theory for max-plus singular values
A Rational Krylov Toolbox for MATLAB
Get PDFThe Rational Krylov Toolbox contains MATLAB implementations of Ruhe's rational Krylov sequence method, algorithms for the implicit and explicit relocation of the poles of a rational Krylov space, an implementation of RKFIT, a robust algorithm for rational least squares fitting, and the RKFUN class for numerical computations with rational functions
Cross-reactive potential of human T-lymphocyte responses in HIV-1 infection
No full textAn effective HIV-1 vaccine should elicit sufficient breadth of immune recognition to protect against the genetically diverse forms of the circulating virus. Evaluation of the breadth and magnitude of cellular immune responses to epitope variants is important for HIV-1 vaccine assessment. We compared HIV-1 Gag-specific T-lymphocyte responses in 20 HIV-1-infected individuals representing two different HIV-1 subtypes, B and C. By assessing T lymphocyte responses with peptides based on natural HIV-1 variants, we found evidence for limited cross-reactivity and significantly enhanced within-clade responses among clade B-infected subjects, and not among clade C-infected subjects
Principles of Remembering and Forgetting
Get PDFWe propose two principles of inductive reasoning related to how observed information is handled by conditioning, and justify why they may be said to represent aspects of rational reasoning. A
partial classification is given of the probability functions which satisfy these principles
Covariance Structure Regularization via Entropy Loss Function
No full textThe need to estimate structured covariance matrices arises in a variety of applications and the problem is widely studied in statistics. A new method is proposed for regularizing the covariance structure of a given
covariance matrix whose underlying structure has been blurred by random noise, particularly when the dimension of the covariance matrix is high. The regularization is made by choosing an optimal structure from an available class of covariance structures in terms of minimizing the discrepancy, defined via the entropy loss function, between the given matrix and the class. A range of potential candidate structures comprising tridiagonal Toeplitz, compound symmetry, AR(1), and banded Toeplitz is considered.
It is shown that for the first three structures local or global minimizers of the discrepancy can be computed by one-dimensional optimization, while for the fourth structure Newton's method enables efficient computation of the global minimizer. Simulation studies are conducted, showing that the proposed new approach provides a reliable way to regularize covariance structures. The approach is also applied to real data analysis, demonstrating the usefulness of the proposed approach in practice