Although there are theorems proved here, I found that most of the material is poorly explained, with little or no motivation at all, certainly insufficient, and their explanations are not very clear. Superficiality is the real problem with this text. Many topics are introduced out of the blue and then forgotten forever, like the Newton-Raphson method, the bisection method and the secant method, which are introduced with virtually no example and then never used in the rest of the book, except for some pointless exercise, or the Cholesky factorization, which is described in such a way that makes its usefulness impossible to understand (again, no clever examples are given). The proofs and the concepts introduced are often foggy and lack of complete rigour, as for example the chapter on orthogonal polynomials, where they instroduce a system of orthogonal polynomials as a basis of the space of polynomials of degree less or equal than n, without ever specifying that, in order to be a basis of a vector space, they should be linearly independent to begin with. The book is full of such imprecisions and superficial treatment of delicate topics, that make its reading a waste of time. Avoid it.
this book is good but it is more likely to be a book for researcher rather than for a student as it is very theoritical so you got to figure out 'how these equations work out' by yourself as the book provides the result not the process. I would recommend numerical linear algebra to those who has little background knowledge of numerical theorem