Generalization of Dodgson's "Virtual Center" Method; an Efficient Method for Determinant Calculation

Authors

  • Elyas Shivanian Department of Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran
Abstract:

Charles Dodgson (1866) introduced a method to calculate matrices determinant, in asimple way. The method was highly attractive, however, if the sub-matrix or the mainmatrix determination is divided by zero, it would not provide the correct answer. Thispaper explains the Dodgson method's structure and provides a solution for the problemof "dividing by zero" called "virtual center".

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

An Efficient Method for Model Reduction in Diffuse Optical Tomography

We present an efficient method for the reduction of model equations in the linearized diffuse optical tomography (DOT) problem. We first implement the maximum a posteriori (MAP) estimator and Tikhonov regularization, which are based on applying preconditioners to linear perturbation equations. For model reduction, the precondition is split into two parts: the principal components are consid...

full text

Calculation of wedged dose distributions using an analytical method

Introduction: Wedge filters are used in radiotherapy to modify photon beam and improve dose uniformity in the target volume. Determination of wedge dose distribution is important to improve treatment planning accuracy. The utilization of treatment planning software to obtain dose distribution is not always available. In this work an analytical model has been developed to calcu...

full text

An algebraic calculation method for describing time-dependent processes in electrochemistry – Expansion of existing procedures

In this paper an alternative model allowing the extension of the Debye-Hückel Theory (DHT) considering time dependence explicitly is presented. From the Electro-Quasistatic approach (EQS) introduced in earlier studies time dependent potentials are suitable to describe several phenomena especially conducting media as well as the behaviour of charged particles (ions) in electrolytes. This leads t...

full text

Fast Bdd Truncation Method for Efficient Top Event Probability Calculation

A Binary Decision Diagram (BDD) [1-3] provides an efficient representation and manipulation of Boolean formulae, and it was shown that a BDD is effective in the diverse fields of computer science and reliability [4]. Bryant [3] popularized the use of a BDD by developing a set of algorithms for an efficient construction and manipulation of BDDs. The BDD algorithm was applied to a reliability ana...

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 12  issue 2

pages  97- 111

publication date 2018-12-01

By following a journal you will be notified via email when a new issue of this journal is published.

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023