As we've journeyed together through the realms of linear algebra, we've uncovered the powers of matrices in transforming shapes and spaces, akin to casting spells that reshape our perception of the ...

Eigenvalues and eigenvectors are foundational concepts in linear algebra, with extensive applications across various domains such as physics, computer graphics, and machine learning. These concepts ...

We consider the numerical calculation of several matrix eigenvalue problems which require some manipulation before the standard algorithms may be used. This includes finding the stationary values of a ...

Abstract Computing the roots of a scalar polynomial, or the eigenvalues of a matrix polynomial, expressed in the Chebyshev basis {𝑇𝑘(𝑥)} is a fundamental problem that arises in many applications.

Recently, in order to find the principal moments of inertia of a large number of rigid bodies, it was necessary to compute the eigenvalues of many real, symmetric 3 × 3 matrices. The available ...

Abstract: The multi-precision methods commonly follow approximate-iterate scheme by first obtaining the approximate solution from a low-precision factorization and solve. Then, they iteratively refine ...

Identification of alcoholism is clinically important because of the way it affects the operation of the brain. Alcoholics are more vulnerable to health issues, such as immune disorders, high blood ...