\n The output variable y (a real number) of a system depends on the input variable x (a real number). We have collected observations y~_i , i = 1,…,N , for N different settings x_i of the input variable, with x_1 < x_2 < \u00b7\u00b7\u00b7 < x_N.We know that the dependence of y on x should be convex and nondecreasing. Formulate the problem of finding new values y_i such that this condition is satisfied and the sum of the squares of adjustments is minimized. Solve the problem for N = 4, input values x_i equal to 1, 2, 4, and 10, and the corresponding observations y~_i equal to 2, 1, 5, and 9.\n <\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"
The output variable y (a real number) of a system depends on the input variable x (a real number). We have collected observations y~_i , i = 1,…,N , for N different settings x_i of the input variable, with x_1 < x_2 < \u00b7\u00b7\u00b7 < x_N.We know that the dependence of y on x should […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_joinchat":[]},"categories":[1],"tags":[],"_links":{"self":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/posts\/227066"}],"collection":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/comments?post=227066"}],"version-history":[{"count":0,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/posts\/227066\/revisions"}],"wp:attachment":[{"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/media?parent=227066"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/categories?post=227066"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/qualityassignments.net\/wp-json\/wp\/v2\/tags?post=227066"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}