The preconditioned inverse iteration [Ney01a] is an efficient method to compute the smallest eigenpair of a symmetric positive definite matrix M . Here we use this method to find the smallest eigenvalues of a hierarchical matrix [Hac99]. The storage complexity of the datasparse H-matrices is almost linear. We use H-arithmetic to precondition with an approximate inverse of M or an approximate Ch...

Due to updating the Lagrangian multiplier twice at each iteration, the symmetric alternating direction method of multipliers (S-ADMM) often performs better than other ADMM-type methods. In practical applications, some proximal terms with positive definite proximal matrices are often added to its subproblems, and it is commonly known that large proximal parameter of the proximal term often resul...

We tackle a fundamental security problem in underwater acoustic networks (UANs). The S-box in the existing block encryption algorithm is more energy consuming and unsuitable for resources-constrained UANs. In this paper, instead of S-box, we present a lightweight, 8-round iteration block cipher algorithm for UANs communication based on chaotic theory and increase the key space by changing the n...

A Markov Decision Process (MDP) is a natural framework for formulating sequential decision-making problems under uncertainty. In recent years, researchers have greatly advanced algorithms for learning and acting in MDPs. This article reviews such algorithms, beginning with well-known dynamic programming methods for solving MDPs such as policy iteration and value iteration, then describes approx...

In linear stability analysis of a large-scale dynamical system, we need to compute the rightmost eigenvalue(s) for a series of large generalized eigenvalue problems. Existing iterative eigenvalue solvers are not robust when no estimate of the rightmost eigenvalue(s) is available. In this study, we show that such an estimate can be obtained from Lyapunov inverse iteration applied to a special ei...

Key concepts [1] Short development iterations (often only a few minutes) Pre-written test cases Each iteration produces code necessary to pass the test cases TDD requires little overhead for the specification of test data, implementing test stubs, test initiation, executing test cases, the interpretation of test results, etc. Well-established development technique in code-centric development Be...

We propose a polynomial time primal dual potential reduction algorithm for linear pro gramming The algorithm generates sequences d and v rather than a primal dual interior point xk sk where di q xi s k i and v k i q xi s k i for i n Only one element of d is changed in each iteration so that the work per iteration is bounded by O mn us ing rank one updating techniques The usual primal dual itera...

Due to update the Lagrangian multiplier twice at each iteration, the symmetric alternating direction method of multipliers (S-ADMM) often performs better than other ADMM-type methods. In practice, some proximal terms with positive definite proximal matrices are often added to its subproblems, and it is commonly known that large proximal parameter of the proximal term often results in “too-small...

The quadratic iteration is mapped using a nondistributive real scator algebra in three dimensions. The bound set S has a rich fractal-like boundary. Periodic points on the scalar axis are necessarily surrounded by off axis divergent magnitude points. There is a one-to-one correspondence of this set with the bifurcation diagram of the logistic map. The three-dimensional S set exhibits selfsimila...

The quadratic iteration is mapped within a non distributive imaginary scator algebra in 1+2 dimensions. The Mandelbrot set is identically reproduced at two perpendicular planes where only the scalar and one of the hypercomplex scator director components is present. However, the bound three dimensional S set projections change dramatically even for very small departures from zero of the second h...