This paper studies convergence properties of the block gmres algorithm when applied to nonsymmetric systems with multiple right-hand sides. A convergence theory is developed based on a representation of the method using matrix-valued polynomials. Relations between the roots of the residual polynomial for block gmres and the matrix "-pseudospectrum are derived, and illustrated with numerical exp...

In this work, we discuss some theoretical and numerical aspects of solving differential equations with discontinuous right-hand sides of Filippov type. In particular: (i) we propose second order corrections to the theory of Filippov, (ii) we provide a systematic and non-ambiguous way to define the vector field on the intersection of several surfaces of discontinuity, and (iii) we propose, and i...

Some three-dimensional analogues of the plane Darboux problems for hyperbolic equations with degeneracy are investigated. In 1954, Protter initiated the study of such threedimensional problems, and it is now well known that for an infinite number of smooth right-hand sides these problems have solutions with a strong power-type singularity on the characteristic cone. This effect appears even for...

We used event-related functional magnetic resonance imaging (fMRI) to investigate the neural correlates of basic interhemispheric visuo-motor integration. In a simple reaction time task, subjects responded to lateralized left and right light flashes with unimanual left and right hand responses. Typically, reaction times are faster for uncrossed responses (that is, visual stimulus and response h...

Many scientific applications require one to solve successively linear systems Ax = b with different right-hand sides b and a symmetric positive definite matrix A. The conjugate gradient method applied to the first system generates a Krylov subspace which can be efficiently recycled thanks to orthogonal projections in subsequent systems. A modified conjugate gradient method is then applied with ...

A 12-year-old girl was visited at our clinic with multiple soft tissue and bony painless swellings over her right hand since she was 2 years old (Figure 1). Soft tissue masses increased in size and number. She was born to non-consanguineous parents. Her early development was normal and she had no other medical problems. There was no family history of similar problem. Examination revealed multip...

We determine a decomposition of the solution fractional difference initial-value problem with periodic right-hand side. For problems S-asymptotically N-periodic side, sufficient condition is proved for existence an solution.

This work is concerned with the development and study of a class of limited memory preconditioners for the solution of sequences of linear systems. To this aim, we consider linear systems with the same symmetric positive definite matrix and multiple right-hand sides available in sequence. We first propose a general class of preconditioners, called Limited Memory Preconditioners (LMP), whose con...