Exercises in Numerical Linear Algebra and Matrix Factorizations. 1st ed. 2020

種類:

電子ブック

責任表示:

by Tom Lyche, Georg Muntingh, Øyvind Ryan

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2020

著者名:

• Lyche, Tom.
• Muntingh, Georg.
• Ryan, Øyvind.
• SpringerLink (Online service)

シリーズ名:

Texts in Computational Science and Engineering ; 23

ISBN:

9783030597894 [303059789X]    

注記:

A Short Review of Linear Algebra -- Diagonally Dominant Tridiagonal Matrices; Three Examples -- Gaussian Eliminationa nd LU Factorizations -- LDL* Factorization and Positive Definite Matrices -- Orthonormal and Unitary Transformations -- Eigenpairs and Similarity Transformations -- The Singular Value Decomposition -- Matrix Norms and Perturbation Theory for Linear Systems -- Least Squares -- The Kronecker Product -- Fast Direct Solution of a Large Linear System -- The Classical Iterative Methods -- The Conjugate Gradient Method -- Numerical Eigenvalue Problems -- The QR Algorithm.
To put the world of linear algebra to advanced use, it is not enough to merely understand the theory; there is a significant gap between the theory of linear algebra and its myriad expressions in nearly every computational domain. To bridge this gap, it is essential to process the theory by solving many exercises, thus obtaining a firmer grasp of its diverse applications. Similarly, from a theoretical perspective, diving into the literature on advanced linear algebra often reveals more and more topics that are deferred to exercises instead of being treated in the main text. As exercises grow more complex and numerous, it becomes increasingly important to provide supporting material and guidelines on how to solve them, supporting students’ learning process. This book provides precisely this type of supporting material for the textbook “Numerical Linear Algebra and Matrix Factorizations,” published as Vol. 22 of Springer’s Texts in Computational Science and Engineering series. Instead of omitting details or mer

ローカル注記:

学内専用E-BOOKS (local access only)