A nonadiabatic steepest descent path method is developed as a qualitative tool to analyze and characterize three different kinetic regimes of electron transfer. In this approach, Miller’s semiclassical instanton solution and Pechukas’ self-consistent treatment of nonadiabatic coupling are applied to the path integral representation of the two-state diffusion equation. The resulting steepest des...

This paper investigates the dynamics of batch learning of multilayer neural networks in the asymptotic case where the number of training data is much larger than the number of parameters. We consider regression problems assuming noisy output data. First, we present experimental results on the behavior in the steepest descent learning of multilayer per-ceptrons and three-layer linear neural netw...

An efficient method to evaluate the surface fields excited on an electrically large dielectric-coated circular cylinder is presented. The efficiency of the method results from the circumferentially propagating representation of the Green’s function as well as its efficient numerical evaluation along a steepest descent path. The circumferentially propagating series representation of the appropri...

The block preconditioned steepest descent iteration is an iterative eigensolver for subspace eigenvalue and eigenvector computations. An important area of application of the method is the approximate solution of mesh eigenproblems for self-adjoint and elliptic partial differential operators. The subspace iteration allows to compute some of the smallest eigenvalues together with the associated i...

We propose here a fully Spice-oriented design algorithm of op-amps for attaining the maximum gains under low power consumptions and assigned slew-rates. Our optimization algorithm is based on a well-known steepest descent method combining with nonlinear programming. The algorithm is realized by equivalent RC circuits with ABMs (analog behavior models) of Spice. The gradient direction is decided...

We introduce a new class of two(multi)-matrix models of positive Hermitean matrices coupled in a chain; the coupling is related to the Cauchy kernel and differs from the exponential coupling more commonly used in similar models. The correlation functions are expressed entirely in terms of certain biorthogonal polynomials and solutions of appropriate Riemann–Hilbert problems, thus paving the way...

By extending the classical analysis techniques due to Samokish, Faddeev and Faddeeva, and Longsine and McCormick among others, we prove the convergence of preconditioned steepest descent with implicit deflation (PSD-id) method for solving Hermitian-definite generalized eigenvalue problems. Furthermore, we derive a nonasymptotic estimate of the rate of convergence of the PSD-id method. We show t...

A general framework is proposed for the study of real-time algorithms. The framework uniies previous algorithmic deenitions of real-time computation. In it, state space traversal is used as a model for computational problems in a real-time environment. The proposed framework also employs a paradigm, known as discrete steepest descent, for algorithms designed to solve these problems. Sequential ...

This paper introduces an algorithm to compute steepest descent paths on multivariate piecewise-linear functions on Euclidean domains of arbitrary dimensions and topology. The domain of the function is required to be a finite PLmanifold modeled by a simplicial complex. Given a starting point in such a domain, the resulting steepest descent path is represented by a sequence of segments terminatin...

Standard backpropagation and many procedures derived from it use the steepest-descent method to minimize a cost function. In this paper, we present a new genetic algorithm, dynamic self-adaptation, to accelerate steepest descent as it is used in iterative procedures. The underlying idea is to take the learning rate of the previous step, to increase and decrease it slightly, to evaluate the cost...