Limit Multiplication Conditions for Existence of Real Roots of Continuous Functions and Implications for Numerical Computation

Year 2017, Volume: 2 Issue: 2, 9 - 16, 30.12.2017

Barış Baykant Alagöz

Abstract

In engineering and applied science, conditions for existence of real roots of a function have useful implications. Solution of many problems such as optimization problems, stability analyses i.e. are based on existence and finding roots of characteristic or objective functions. This theoretical study presents limit conditions for existence of at least one real root of a continuous and differentiable function. These conditions are an elaboration of intermediate value theorem and Rolle’s theorem on the bases of limit theorem. The proposed conditions can be useful to numerical check or ensure the existence of real root solution of very complex engineering and science problems without solving the complicated equations. Computer based design and analysis tools may benefit from these conditions in solution of complicated engineering problems. 

Keywords

Real roots, continuous functions, limit conditions, numerical methods

Sürekli Fonksiyonların Gerçek Köklerinin Olması İçin Limit Çarpma Koşulları ve Sayısal Hesaplama İçin Uygulaması

Abstract

Mühendislik ve uygulamalı bilimlerde, bir fonksiyonun gerçek köklerinin var olma koşullarının faydalı uygulamaları olur. Optimizasyon problemleri, kararlılık analizleri gibi bir çok problemin çözümü karakteristik veya objektif fonksiyonların köklerinin varlığına veya bulunabilmesine dayanır. Bu teorik çalışma, sürekli ve türevlenebilir bir fonksiyonun en azından bir gerçek kökünün varolabilmesi için sınır koşullarını sunmaktadır. Bu koşullar,  ara değer teoremi ve Rolle teoreminin limit koşullarda incelemesine dayanır. Önerilen koşullar, karmaşık mühendislik  denklemlerini çözmeden  gerçek köklerin varlığının nümerik olarak kontrol edilmesi veya garanti edilebilmesi için faydalı olabilir. Bilgisayar tabanlı tasarım ve analiz araçları karmaşık mühendislik problemlerinin çözümünde bu koşullardan yararlanabilir.

Keywords

Reel Kökler, Sürekli Fonksiyonlar, Limit koşullar, Numerik Yöntemler

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