By G. W. Stewart

This can be a good common creation to numerical research, purely simple math is needed. it really is enjoyable and straightforward to learn. this can be a "small" booklet; the most important part (linear equations) being sixty six pages. even if, it does disguise loads of ground.

Code fragments are in C and FORTRAN. The C code evidently hasn't been confirmed (abs() rather than fabs() throughout). there are various typos within the textual content in addition to within the code fragments.

**Read Online or Download Afternotes on numerical analysis: a series of lectures on elementary numerical analysis presented at the University of Maryland at College Park and recorded after the fact PDF**

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**Extra info for Afternotes on numerical analysis: a series of lectures on elementary numerical analysis presented at the University of Maryland at College Park and recorded after the fact**

**Example text**

A problem with c. if (sign(fb) == sign(fc)){ c = a; fc = fa; } 14. 2). 15. Finally, we return after leaving the while loop. } return; 16. 1. Here d is always on the side of x* that is opposite c, and the value of c is not changed by the iteration. This means that although b is converging superlinearly to x*, the length of the bracket converges to a number that is greater than zero — presumably much greater than eps. Thus the algorithm cannot converge until its erratic asymptotic behavior forces some bisection steps.

Second, the procedure requires one extra function evaluation per iteration. This is a serious problem if function evaluations are expensive. 2. The key to the secant method is to observe that once the iteration is started we have two nearby points, Xk and x^-i, where the function has been evaluated. 2) This iteration is called the secant method. 1. The secant method. 3. The secant method derives its name from the following geometric interpretation of the iteration. Given XQ and xi, draw the secant line through the graph of / at the points (XQ,/(XQ)) and (#1,/(xi)).

Armed with this result, we can return to Newton's method and the constant slope method. For Newton's method we have (remember that /'(#*) is assumed to be nonzero). Thus Newton's method is seen to be at least quadratically convergent. Since Newton's method will converge faster than quadratically only when f " ( x * ) = 0. 3). 24 Afternotes on Numerical Analysis Multiple zeros 17. Up to now we have considered only a simple zero of the function /, that is, a zero for which /'(#*) ^ 0. We will now consider the case where By Taylor's theorem where £x lies between x* and x.