Iterated function systems have been powerful tools to generate fractals. However, the requirement of using the same maps at every iteration results in a fractal that may be too self-similar for certain applications. We present a construction in which the maps are allowed to be updated at each iteration in order to generate more general fractals without changing the computational complexity. We ...

In this paper we propose two modifications to Nesterov’s algorithms for minimizing convex functions in relative scale. The first is based on a bisection technique and leads to improved theoretical iteration complexity and the second is a heuristic for avoiding restarting behavior. The fastest of our algorithms produces a solution within relative error O(1/k) of the optimum, with k being the ite...

This paper describes the results of using genetic programming with bounded iteration constructs, which allow the computational complexity of the solution to be an emergent property. It is shown that such operators render the even-6-parity problem trivial, and the results of experiments with other, harder, problems that require O(n) complexity are shown. This method is contrasted with Automatica...

The theory of optimal algorithmic processes is part of computational complexity. This paper deals with analytic computational complexity. The relation between the goodness of an iteration algorithm and its new function evaluation and memory requirements are analyzed. A new conjecture is stated.

The learning with errors (LWE) problem is one of the main mathematical foundations post-quantum cryptography. One groups algorithms for solving LWE Blum–Kalai–Wasserman (BKW) algorithm. This paper presents new improvements BKW-style instances. We target minimum concrete complexity, and we introduce a reduction step where partially reduce last position in an iteration finish next iteration, allo...

ABS methods are direct iterative methods for solving linear systems of equations, where the i-th iteration satisfies the first i equations. Thus, a system of m equations is solved in at most m ABS iterates. In 2004 and 2007, two-step ABS methods were introduced in at most [((m+1))/2] steps to solve full row rank linear systems of equations. These methods consuming less space, are more compress ...

We propose new versions of accelerated first order methods for convex composite optimization, where the prox parameter is allowed to increase from one iteration to the next. In particular we show that a full backtracking strategy can be used within the FISTA [1] and FALM algorithms [7] while preserving their worst-case iteration complexities of O( √ L(f)/ ). In the original versions of FISTA an...

A new nonlinear solution method is developed and applied to a non-equilibrium radiation di!usion problem. With this new method, Newton-like super-linear convergence is achieved in the nonlinear iteration, without the complexity of forming or inverting the Jacobian from a standard Newton method. The method is a unique combination of an outer Newton-based iteration and and inner conjugate gradien...

Abstract — Digital signal processing algorithms are repetitive in nature. These algorithms are described by iterative data-flow graphs where nodes represent computations and edges represent communications. For all data-flow graphs, there exists a fundamental lower bound on the iteration period referred to as the iteration bound. Determining the iteration bound for signal processing algorithms d...