Contour integration schemes are a valuable tool for the solution of difficult interior eigenvalue problems. However, many large linear systems with multiple right hand sides may prove prohibitive computational expense. The number sides, and thus, cost be reduced if projected subspace is created using moments. In this work, we explore heuristics choice application moments respect to various othe...

A right-brain damaged patient with pure tactile extinction was asked to report series of single or double light, brief touches delivered to both hands, the thumb or the pinkie of a single hand, the sides of a single index. The stimulated hand was positioned palm up or palm down, in front of or behind the patient, in anatomic or crossed position. In double touch conditions, stimuli coded as left...

We propose a variant of GMRES, where multiple (two or more) preconditioners are applied simultaneously, while maintaining minimal residual optimality properties. To accomplish this, a block version of Flexible GMRES is used, but instead of considering blocks associated with multiple right hand sides, we consider a single right-hand side and grow the space by applying each of the preconditioners...

OBJECTIVE We described the frequency and distribution of keyboard users' potentially risky postural behaviors. METHOD Forty-three participants' keyboard postural behaviors were rated with the Keyboard-Personal Computer Style instrument (Baker & Redfern, 2005). The frequency and distribution of keyboard postural behaviors and the associations and differences between the right and left sides we...

We present a deflated version of the conjugate gradient algorithm for solving linear systems. The new algorithm can be useful in cases when a small number of eigenvalues of the iteration matrix are very close to the origin. It can also be useful when solving linear systems with multiple right-hand sides, since the eigenvalue information gathered from solving one linear system can be recycled fo...

We study the Lanczos method for solving symmetric linear systems with multiple right-hand sides. First, we propose a numerical method of implementing the Lanczos method, which can provide all approximations to the solution vectors of the remaining linear systems. We also seek possible application of this algorithm for solving the linear systems that occur in continuation problems. Sample numeri...

Block-GMRES is an iterative method for solving nonsymmetric systems of linear equations with multiple right-hand sides. Restarting may be needed, due to orthogonalization expense or limited storage. We discuss how restarting affects convergence and the role small eigenvalues play. Then a version of restarted block-GMRES that deflates eigenvalues is presented. It is demonstrated that deflation c...

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 GMHES and the matrix &-pseudospectrum are derived, and illustrated with numerical exp...