Numerical Linear Algebra and Optimization, Vol. 1

by Philip E. Gill, Walter Murray, Margaret H. Wright

Numerical Linear Algebra and Optimization, Volume 1 details numerical methods for linear systems, linear least-squares and linear programming. It introduces the fundamental principles of scientific computing and stresses the importance of these ideas in numerical linear algebra.

Hardcover

First published September 1, 1990

Reviews

[Mohamad Fazeli · Rating 5 out of 5]

I used it as the textbook for a graduate course in Sharif University of Technology about numerical linear algebra so the explanation is just according so those part and the section on optimization is omitted.
It is very good.
By avoiding proof of more complex theoretical arguments, It gained space for more elaboration on algorithms, providing the reader with a detailed examination of edge cases.
In contrast with Numerical Linear Algebra Numerical Linear Algebra, This book has less theoretical depth, yet it has the vast examination of algorithms, for example for solving different types of linear systems of equations Gill et al. provided in-depth explanation of edge cases and different sizes of matrices with different ranks, but Trefethen et al. just assumed rows is going to be more than columns and ignored other cases, again this is the case for least squares problems. But this book has a detailed examination of the condition number of least squares problem while Gill et al.'s book just skimmed over it.
Numerical Linear Algebra And Optimization doesn't explain algorithms for finding eigenvalues and eigenvectors, moreover, it doesn't explain anything about iterative methods for solving any problems.