[randusername]

For anyone turned off by this document and its proofs, I recommend Numerical Methods for Scientists and Engineers (Hamming). Still a math text, but more approachable.

The five key ideas from that book, enumerated by the author:

(1) the purpose of computing is insight, not numbers

(2) study families and relationships of methods, not individual algorithms

(3) roundoff error

(4) truncation error

(5) instability

[ses1984]

Can you elaborate a little on what 1 is supposed to mean?

[randusername]

> This motto is often thought to mean that the numbers from a computing machine should be read and used, but there is much more to the motto. The choice of the particular formula, or algorithm, influences not only the computing but also how we are to understand the results when they are obtained. The way the computing progresses, the number of iterations it requires, or the spacing used by a formula, often sheds light on the problem...Thus computing is, or at least should be, intimately bound up with both the source of the problem and the use that is going to be made of the answers-- it is not a step to be taken in isolation from reality

(From "An Essay on Numerical Methods" p 3 of the mentioned text; emphasis authors)

[anymouse123456]

Not the OP, but I suspect it means focus on what questions are being asked first, and even then, look for opportunities to simplify wherever you find them.

So many of us spend so much time getting enamoured with technical solutions to problems that no one cares about.