In this section, we will show you how to calculate the upper and lower bounds in Excel. There are various ways you can calculate the upper and lower bounds. However, we are going to show you one of the simplest and reliable ways. For the record, that would be by constructing a confide...
The advantages of the method are that it gives upper and lower bounds of comparable accuracy, the wave equation need not be separable, and the method can be applied to excited states as well as ground states. So far, we have used series type solutions, so that no integrations or secular ...
An intermediate theorem for the Fokker-Planck equation is presented for the first time from which lower bounds for the eigenvalues can be extracted. The same theorem can be applied to the master equation in detailed balance. We discuss as a first application the lower and upper bounds for the...
We derive analytical lower and upper bounds for the entanglement Rényi-α entropy of arbitrary dimensional bipartite quantum systems. We also demonstrate the application our bound for some concrete examples. Moreover, we establish the relation between entanglement Rényi-α entropy and some other ...
In this paper we derive lower and upper bounds on the excess risk of stochastic optimization of exponentially concave loss functions. Exponentially concave loss functions encompass several fundamental problems in machine learning such as squared loss in linear regression, logistic loss in classification, ...
The nef cone of a projective variety Y is an important and often elusive invariant. In this paper we construct two polyhedral lower bounds and one polyhedral upper bound for the nef cone of Y using an embedding of Y into a toric variety. The lower bounds generalize the combinatorial descripti...
We propose lower and upper bounds for the KL divergence, which lead to a new approximation and interesting insights into previously proposed approximations. An application to the comparison of speaker models also shows how such approximations can be used to validate assumptions on the models. 展开 ...
In addition we present a new distributed algorithm for solving general covering and packing linear programs. For some problems this algorithm is tight with the lower bounds, for others it is a distributed approximation scheme. Together, our lower and upper bounds establish the local computability ...
This paper presents a new method for computing upper and lower bounds for the eigenvalues of the system [ r( x) y′]′ + λp( x) y = 0, y( a) = y( b) = 0. It permits one to approximate as closely as desired simultaneously to any finite subset of the eigenvalues, and the ...
Local Computation: Lower and Upper Bounds Fabian Kuhn, Thomas Moscibroda, Roger Wattenhofer Journal of the ACM|March 2016, Vol 63(2) Publication Download BibTex The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed sys...