The branching of un,symmetric equilibrium states from axisymmetric equilibrium states for clamped circular plates subjected to a uniform edge thrust and a uniform lateral pressure is analyzed in this paper. The branching process is called wrinkling and the loads at which branching occurs are called wrinkling loads. The nonlinear von Karman plate theory is employed. The wrinkling loads are deter...

The power method and block Lanczos method are popular numerical algorithms for computing the truncated singular value decomposition (SVD) and eigenvalue decomposition problems. Especially in the literature of randomized numerical linear algebra, the power method is widely applied to improve the quality of randomized sketching, and relative-error bounds have been well established. Recently, Musc...

The core computational step in spectral learning – finding the projection of a function onto the eigenspace of a symmetric operator, such as a graph Laplacian – generally incurs a cubic computational complexity O(N). This paper describes the use of Lanczos eigenspace projections for accelerating spectral projections, which reduces the complexity to O(nTop + nN) operations, where n is the number...

The one-hole spectral weight for two chains and two dimensional lattices is studied numerically using a new method of analysis of the spectral function within the Lanczos iteration scheme: the Lanczos spectra decoding method. This technique is applied to the t−Jz model for Jz → 0, directly in the infinite size lattice. By a careful investigation of the first 13 Lanczos steps and the first 26 on...

We present a variant of the popular BiCGSTAB method for solving nonsymmetric linear systems. The method, which we denote by ML(k)BiCGSTAB, is derived from a variant of the BiCG method based on a Lanczos process using multiple (k > 1) starting left Lanczos vectors. Compared with the original BiCGSTAB method, our new method produces a residual polynomial which is of lower degree after the same nu...

We increase the efficiency of a recently proposed time integration scheme for time dependent quantum transport by using the Lanczos method for time evolution. We illustrate our modified scheme in terms of a simple one dimensional model. Our results show that the Lanczos-adapted scheme gives a large increase in numerical efficiency, and is an advantageous route for numerical time integration in ...

Recently, there has been a revival of interest in the Lanczos potential of the Weyl conformal tensor. Previous work by Novello and Neto has been done with the linearized Lanczos potential as a model of a spin-2 field, which depends on a massless limit of the field. In this paper, we look at an action based on a massless potential, and show that it is classically equivalent to the linearized reg...

The solution of linear systems with a parameter is an important problem in engineering applications, including structural dynamics, acoustics, and electronic circuit simulations, and in related model order reduction methods such as Padé via Lanczos. In this paper, we present a Lanczos-based method for solving parameterized symmetric linear systems with multiple right-hand sides. We show that fo...

New restarted Lanczos bidiagonalization methods for the computation of a few of the largest or smallest singular values of a large matrix are presented. Restarting is carried out by augmentation of Krylov subspaces that arise naturally in the standard Lanczos bidiagonalization method. The augmenting vectors are associated with certain Ritz or harmonic Ritz vectors. Computed examples show the ne...

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...