Nonlinear evolution equations governed by m-accretive operators in Banach spaces are discretized via the backward or forward Euler methods with variable stepsize. Computable a posteriori error estimates are derived in terms of the discrete solution and data, and shown to converge with optimal order O( √ τ). Applications to scalar conservation laws and degenerate parabolic equations (with or wit...

In this paper, we propose a generic and simple algorithmic framework for first order optimization. The framework essentially contains two consecutive steps in each iteration: 1) computing and normalizing the mini-batch stochastic gradient; 2) selecting adaptive step size to update the decision variable (parameter) towards the negative of the normalized gradient. We show that the proposed approa...

A new type of variable coefficient Runge-Kutta-Nyström methods is proposed for solving the initial value problems of the special form y(t) = f(t, y(t)). The method is based on the exact integration of some given functions in order to solve the problem exactly when the solution is the linear combination of these functions. If this is not the case, the algebraic order (order of accuracy) of the m...

Numerical difficulties encountered when following paths using methods such as homotopy continuation may be overcome by combining adaptive stepsize and adaptive multiprecision. In the paper Adaptive multiprecision path tracking [1], precision and stepsize are adapted separately. This can lead to suboptimal performance and even failure in certain circumstances. This paper presents a strategy for ...

Modulus Algorithms for Blind Equalization Constantinos B. Papadias e-mail: [email protected] Dirk T. M. Slock e-mail: [email protected] Institut EURECOM, 2229 route des Crêtes, Sophia Antipolis, 06560 Valbonne, FRANCE Abstract One of the most known classes of algorithms for blind equalization is the so-called class of Constant Modulus Algorithms (CMA's) [1], [2]. These adaptive algorithms use ...

Abstract This work introduces a new one-step method with three intermediate points for solving stiff differential systems. These types of problems appear in different disciplines and, particular, derived from chemical reactions. In fact, the term “stiff”’ was coined by Curtiss and Hirschfelder an article on kinetics (Hirschfelder, Proc Natl Acad Sci USA 38:235–243, 1952). The techniques interpo...

We present a semi-public key implementation of quantization index modulation (QIM) watermarking called Secure QIM (SQIM). Given a signal, a watermark detector can learn the presence of an SQIM watermark without learning anything anything else from the detection process. The watermark detector first transforms the signal with a secret transform, unknown to the detector, and then quantizes the tr...

An unconditionally energy stable time stepping scheme is introduced to solve CahnMorral-like equations in the present study. It is constructed based on the combination of David Eyre’s time stepping scheme and Schur complement approach. Although the presented method is general and independent to the choice of homogeneous free energy density function term, logarithmic and polynomial energy functi...

Variable-step variable-order 3-stage Hermite–Birkhoff–Obrechkoff methods of order 4 to 14, denoted by HBO(4-14)3, are constructed for solving non-stiff systems of first-order differential equations of the form y′ = f(x, y), y(x0) = y0. These methods use y′ and y′′ as in Obrechkoff methods. Forcing a Taylor expansion of the numerical solution to agree with an expansion of the true solution leads...