Communities in DSpace

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Perturbation Theory and Eigenvalue Localization for Quaternionic Matrices
(Book Rivers, 2025) Istkhar Ali, Mohammad Waquas Khadim
"This chapter presents a comprehensive exploration of perturbation theory and eigenvalue localization for matrices over the quaternion division algebra, addressing key theoretical and computational challenges arising from their non-commutative nature. Building on recent advances in quaternionic linear algebra, we extend classical perturbation results-such as the Bauer-Fike theorem and relative eigenvalue bounds-to the quaternionic setting, with a focus on both right and left eigenvalues, which exhibit fundamentally distinct behaviors. We derive new perturbation bounds for structured quaternionic matrices (e.g., Hermitian, unitary, and skew-Hermitian), leveraging their unique spectral properties."
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Numerical Solutions of Non-Linear Equations by Newton’s, Steffensen’s & Halley’s Method
(Book Rivers, 2025) Najmuddin Ahmad
"In his chapter, Numerical analysis is the study of algorithms that use numerical approximation for the problem of mathematical analysis."
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Goal Programming
(Book Rivers, 2025) Quazzafi Rabbani
"In this chapter, we discussed Goal Programming (GP) is the most widely and suitable technique for solving multi-objective linear problems."
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Non-linear Equations and Their Numerical Solution by Fast Convergent Methods
(Book Rivers, 2025) Abdul Wadood Khan
"In his chapter, Numerical analysis is the study of algorithms that use numerical approximation for the problem of mathematical analysis. These are used in solving scientific and engineering problems which has increased dramatically in modern time. Numerical methods are often used to obtain the approximate solution of such problem in which it is not possible to obtain exact solution."
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Graph Theory
(Book Rivers, 2025) Shadab Ahmad Khan
"In this chaper, Graph Theory is a fundamental area of discrete mathematics that studies the relationships between pairs of objects. These objects are represented as vertices (or nodes), and the connections between them are known as edges (or links). Originating Königsberg bridge problem in the 18th century, Graph Theory has since evolved into a powerful mathematical framework with broad applications."