Least ascent

In general, both methods do not yield the same results. The second method (ii) produces additional curves which are other (artificial) solutions of the GE equation which do not characterize valley floors. It should be noted that there are some simplifications of (ii) when following a given eigenvector of the Hessian by the so-called stream bed method, see [3-5]. SDP and least ascent path (VF-GE) have each certain advantages as well as limitations. 

Acute mountain sickness PO 500-1000 mg/day in divided doses, if possible, begin 24-48 hr before ascent continue at least 48 hr at high altitude. Initially, 250 mg 2 times/day use lowest effective dose. 

Now a new case is calculated at the best previous point and a new direction of steepest ascent is determined. The process is repeated as many times as seems advisable. The entire procedure is susceptible to automatic treatment on the computer. The only point of uncertainty is the size of the steps to be taken. It may be necessary to revise this from time to time depending upon the progress of the study. As the optimum is approached, the steps should decrease in size. Even if it is decided that for a particular problem and a particular computer completely automatic calculation is impractical, at least some fairly large combination of operations can be programmed for one computer run. 

Following application of the method of steepest ascents, it will usually be advisable to investigate the neighborhood of the optimum more carefully, fitting at least a second-degree polynomial to the response surface as described in Section VI B. 

Let us analyze the previous case by taking into account the third factor X,. The outcomes of FUFE 23 and the results of application of method of steepest ascent are given in Table 2.216. Thirteen trials were necessary to reach the maximal yield of 85.2%. The outcomes of the simplex method are in Table 2.217. Maximal yield after 14 trials is 85.0%. Approximately the same number of trials has been necessary by both methods to reach the optimum. It should be stressed once again that FUFE requires replications, so that to reach optimum by the method of steepest ascent, we need at least twice as many trials. Evidently, a half-replica instead of FUFE in the basic experiment may reduce the number of trials. However, there is a possibility of wrong direction of the movement to optimum due to the possible effects of interactions. 

Altitude sickness PO 250 mg two to four times/day. If possible begin 24-48 hours before ascent continue for at least 48 hours at high altitude as needed to control symptom... 

If a cricket ball be thrown up into the air, its velocity, ds/dt, will go on diminishing until the ball reaches the highest point of its ascent. Its velocity will then be zero. After this, the velocity of the ball will increase until it is caught in the hand. In other words, ds/dt is first positive, then zero, and then negative. This means that the distance, s, of the ball from the ground will be greatest when ds/dt is least s will be a maximum when ds/dt is zero. 

From the simplified case A, which we discussed above, it must be concluded that at least two different MEPs can be defined, one for the ascent and one for the descent (within the same coordinate system). 

---