The period estimation and periodic decomposition of a signal are the long-standing problems in the field of signal processing and biomolecular sequence analysis. To address such problems, we introduce the Ramanujan subspace pursuit (RSP) based on the Ramanujan subspace. As a greedy iterative algorithm, the RSP can uniquely decompose any signal into a sum of exactly periodic components, by selec...

In this paper, we propose a new adaptive algorithm for subspace estimation and tracking that is based on Rayleigh’s quotient. This algorithm allows the estimation of the signal subspace of a vector sequence. It has a number of interesting properties such as a low computational complexity, a fast convergence, orthogonality of the subspace vectors which is ensured at each iteration and a good num...

In this paper we define and study new directional Metropolis–Hastings algorithms that propose states in hyperplanes. Each iteration in directional Metropolis–Hastings algorithms consist of three steps. First a direction is sampled by an auxiliary variable. Then a potential new state is proposed in the subspace defined by this direction and the current state. Lastly, the potential new state is a...

We discuss the close connection between eigenvalue computation and optimization using the Newton method and subspace methods. From the connection we derive a new class of Newton updates. The new update formulation is similar to the well-known Jacobi-Davidson method. This similarity leads to simplified versions of the Jacobi-Davidson method and the inverse iteration generalized Davidson (IIGD) m...

Solving the electronic structure problem for nanoscale systems remains a computationally challenging problem. The numerous degrees of freedom, both electronic and nuclear, make the problem impossible to solve without some effective approximations. Here we illustrate some advances in algorithm developments to solve the Kohn-Sham eigenvalue problem, i.e. we solve the electronic structure problem ...

Normal mode analysis plays an important role in relating the conformational dynamics of proteins to their biological function. The subspace iteration method is a numerical procedure for normal mode analysis that has enjoyed widespread success in the structural mechanics community due to its numerical stability and computational efficiency in calculating the lowest normal modes of large systems....

This paper presents an a posteriori error estimator for the preconditioned iteration scheme of Bramble, Knyazev and Pasciak to compute the smallest eigenvalues together with its invariant subspace of an elliptic diierential operator. The error estimator is applied both to the nite element space in which the preconditioned iteration is performed (iteration error estimation) as well as to its hie...

For a given blur, we apply a fixed point method to solve the total variation-based image restoration problem. A new algorithm for the discretized system is presented. Convergence of outer iteration is efficiently improved by adding a linear term on both sides of the system of nonlinear equations. In inner iteration, an algebraic multigrid (AMG) method is applied to solve the linearized systems ...