{"action":"created","issue":{"url":"https://api.github.com/repos/uwhpsc-2016/homework1/issues/26","repository_url":"https://api.github.com/repos/uwhpsc-2016/homework1","labels_url":"https://api.github.com/repos/uwhpsc-2016/homework1/issues/26/labels{/name}","comments_url":"https://api.github.com/repos/uwhpsc-2016/homework1/issues/26/comments","events_url":"https://api.github.com/repos/uwhpsc-2016/homework1/issues/26/events","html_url":"https://github.com/uwhpsc-2016/homework1/issues/26","id":147192111,"number":26,"title":"Exercise #2: convergence criterion and scaling factor","user":{"login":"chengdang","id":18148322,"avatar_url":"https://avatars.githubusercontent.com/u/18148322?v=3","gravatar_id":"","url":"https://api.github.com/users/chengdang","html_url":"https://github.com/chengdang","followers_url":"https://api.github.com/users/chengdang/followers","following_url":"https://api.github.com/users/chengdang/following{/other_user}","gists_url":"https://api.github.com/users/chengdang/gists{/gist_id}","starred_url":"https://api.github.com/users/chengdang/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/chengdang/subscriptions","organizations_url":"https://api.github.com/users/chengdang/orgs","repos_url":"https://api.github.com/users/chengdang/repos","events_url":"https://api.github.com/users/chengdang/events{/privacy}","received_events_url":"https://api.github.com/users/chengdang/received_events","type":"User","site_admin":false},"labels":[{"url":"https://api.github.com/repos/uwhpsc-2016/homework1/labels/Answered","name":"Answered","color":"c2e0c6"}],"state":"open","locked":false,"assignee":null,"milestone":null,"comments":3,"created_at":"2016-04-10T04:31:25Z","updated_at":"2016-04-11T18:56:03Z","closed_at":null,"body":"I have two questions regarding Exercise #2:\r\n(1) I guess I'm puzzled by the convergence criterion given in Exercise #2, step 4:\r\n....\r\n       While abs(x_k+1 - x_k)  > epsilon\r\n.....\r\nShouldn this be:  abs ( f(x_k+1) - f(x_k) ) > epsilon? \r\nI assume it is derived from the mathematical request of df/dx  =  0, in practice, abs(df) <= epsilon\r\n\r\n(2) The scaling factor, should be the 'step' size that we chose to modify x_k in each step. Ideally it needs to be small enough, but why should it be smaller than 1, not 0.5 or 2, in this specific case? per request in test 4.\r\n\r\nThank you!\r\n"},"comment":{"url":"https://api.github.com/repos/uwhpsc-2016/homework1/issues/comments/208498352","html_url":"https://github.com/uwhpsc-2016/homework1/issues/26#issuecomment-208498352","issue_url":"https://api.github.com/repos/uwhpsc-2016/homework1/issues/26","id":208498352,"user":{"login":"quantheory","id":1740206,"avatar_url":"https://avatars.githubusercontent.com/u/1740206?v=3","gravatar_id":"","url":"https://api.github.com/users/quantheory","html_url":"https://github.com/quantheory","followers_url":"https://api.github.com/users/quantheory/followers","following_url":"https://api.github.com/users/quantheory/following{/other_user}","gists_url":"https://api.github.com/users/quantheory/gists{/gist_id}","starred_url":"https://api.github.com/users/quantheory/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/quantheory/subscriptions","organizations_url":"https://api.github.com/users/quantheory/orgs","repos_url":"https://api.github.com/users/quantheory/repos","events_url":"https://api.github.com/users/quantheory/events{/privacy}","received_events_url":"https://api.github.com/users/quantheory/received_events","type":"User","site_admin":false},"created_at":"2016-04-11T18:56:03Z","updated_at":"2016-04-11T18:56:03Z","body":"For sigma, you typically want to pick a \"small\" value, but what that means depends on the problem; I believe that you're correct that 1 is a somewhat arbitrary limit for the purposes of this problem. Note for instance that if x and f(x) have physical units, sigma is not dimensionless, so an appropriate value of sigma must depend on the relative magnitude of f, f', and x given the choice of units for a particular problem."}}