相关论文: Three New Arnoldi-Type Methods for the Quadratic E…

We investigate the generalized second-order Arnoldi (GSOAR) method, a generalization of the SOAR method proposed by Bai and Su [{\em SIAM J. Matrix Anal. Appl.}, 26 (2005): 640--659.], and the Refined GSOAR (RGSOAR) method for the quadratic…

We consider a large-scale quadratic eigenvalue problem (QEP), formulated using P1 finite elements on a fine scale reference mesh. This model describes damped vibrations in a structural mechanical system. In particular we focus on problems…

A new approach is presented to compute the seismic normal modes of a fully heterogeneous, rotating planet. Special care is taken to separate out the essential spectrum in the presence of a fluid outer core. The relevant…

The randomized Arnoldi process has been used in large-scale scientific computing because it produces a well-conditioned basis for the Krylov subspace more quickly than the standard Arnoldi process. However, the resulting Hessenberg matrix…

The partial Schur factorization can be used to represent several eigenpairs of a matrix in a numerically robust way. Different adaptions of the Arnoldi method are often used to compute partial Schur factorizations. We propose here a…

A novel linear-algebraic algorithm, multiple Arnoldi method, was developed in an interdisciplinary study between physics and applied mathematics and realized one-hundred-million-atom (100-nm-scale) electronic state calculations on the K…

It is shown that the problem of balancing a nonnegative matrix by positive diagonal matrices can be recast as a constrained nonlinear multiparameter eigenvalue problem. Based on this equivalent formulation some adaptations of the power…

In recent years, a great deal of attention has been focused on numerically solving exponential integrators. The important ingredient to the implementation of exponential integrators is the efficient and accurate evaluation of the so called…

In this work, we explore the application of multilinear algebra in reducing the order of multidimentional linear time-invariant (MLTI) systems. We use tensor Krylov subspace methods as key tools, which involve approximating the system…

An efficient way of solving 2D stability problems in fluid mechanics is to use, after discretization of the equations that cast the problem in the form of a generalized eigenvalue problem, the incomplete Arnoldi-Chebyshev method. This…

In this research, we solve polynomial, Sobolev polynomial, rational, and Sobolev rational least squares problems. Although the increase in the approximation degree allows us to fit the data better in attacking least squares problems, the…

We propose subspace methods for 3-parameter eigenvalue problems. Such problems arise when separation of variables is applied to separable boundary value problems; a particular example is the Helmholtz equation in ellipsoidal and…

In this paper we extend the Residual Arnoldi method for calculating an extreme eigenvalue (e.g. largest real part, dominant,...) to the case where the matrices depend on parameters. The difference between this Arnoldi method and the…

We propose an acceleration scheme for first-order methods (FOMs) for convex quadratic programs (QPs) that is analogous to Anderson acceleration and the Generalized Minimal Residual algorithm for linear systems. We motivate our proposed…

A previously developed quantum reduced-order model is revised and applied, together with the domain decomposition, to develop the quantum element method (QEM), a methodology for fast and accurate simulation of quantum eigenvalue problems.…

An efficient and robust restart strategy is important for any Krylov-based method for eigenvalue problems. The tensor infinite Arnoldi method (TIAR) is a Krylov-based method for solving nonlinear eigenvalue problems (NEPs). This method can…

Operator-theoretic analysis of nonlinear dynamical systems has attracted much attention in a variety of engineering and scientific fields, endowed with practical estimation methods using data such as dynamic mode decomposition. In this…

Arnoldi method and conjugate gradient method are important classical iteration methods in solving linear systems and estimating eigenvalues. Their efficiency often affected by the high dimension of the space, where quantum computer can play…

We present a sampling strategy suitable for optimization problems characterized by high-dimensional design spaces and noisy outputs. Such outputs can arise, for example, in time-averaged objectives that depend on chaotic states. The…

A new solution strategy for quadratic eigenvalue problems, and the derivatives of the eigenvalues, is proposed, by combining the generalized reduction method with dual numbers. To demonstrate the method, we use the quadratic eigenvalue…