False position method those relatively unusual unfavorable situations. The failure mode is easy to detect (the same end-point is retained twice in a row) and easily remedied by next picking a modified false position, such as or down-weighting one of the endpoint values to force the next to occur on that side of the function. The factor of 2 above looks arbitrary, but it guarantees superlinear convergence (asymptotically, the algorithm will perform two regular steps after any modified step, and has order of convergence 1.442). There are other ways to pick the rescaling which give even better superlinear convergence rates. The above adjustment
Always True to You in My Fashion own sick way, I'll always stay true to you". Always True to You in My Fashion "Always True to You in My Fashion" is a 1948 show tune by Cole Porter, written for the musical "Kiss Me, Kate". It is based on "Non Sum Qualis Eram Bonae sub Regno Cynarae," a similarly ironic poem by the English Decadent poet Ernest Dowson (1867–1900), which has the refrain 'I have been faithful to thee, Cynara, in my fashion,' and which was probably inspired by Dowson's lifelong friend Adelaide Foltinowicz, who never returned his devotion. The phrase "faithful in my fashion" entered the