Adaptive Machine Learning Algorithms with Python: Solve Data Analytics and Machine Learning Problems on Edge Devices

© The Author(s), under exclusive license to APress Media, LLC, part of Springer Nature 2022

C. ChatterjeeAdaptive Machine Learning Algorithms with Pythonhttps://doi.org/10.1007/978-1-4842-8017-1_7

7. Generalized Eigenvectors

Chanchal Chatterjee¹  

(1)

San Jose, CA, USA

 

7.1 Introduction and Use Cases

This chapter is concerned with the adaptive solution of the generalized eigenvalue problems AΦ=BΦΛ, ABΦ=ΦΛ, and BAΦ=ΦΛ, where A and B are real, symmetric, nXn matrices and B is positive definite. In particular, we shall consider the problem AΦ=BΦΛ, although the remaining two problems are similar. The matrix pair (pencil) (A,B) is commonly referred to as a symmetric-definite pencil [Golub and VanLoan 83].

As seen before, the conventional (numerical analysis) ...