Theorem: Convergence of Newton’s Method

May 19th, 2015
Studypool Tutor
Price: $10 USD

Tutor description

F ϵ C2 [a,b], Ǝ r ϵ [a,b], for which f(r)=0, and f’(r)≠0; then Ǝ δ>0, such that ɏ r0 ϵ [r-δ,r+δ] The Newton’s sequence will converge to r..Secant Method From r = r_0 – (f(r_0))/(f’(r_0))

Word Count: 178
Showing Page: 1/2
Newtons IterationAlgorithm:While |r1-r0| > er0 r1r1 r0 f(r0)/f(r0)EndNeeds:f is C2f has to be availabler0 starting point: difficult to findTheorem: Convergence of Newtons MethodF C2 [a,b], r [a,b], for which f(r)=0, and f(r)0; then >0, such that r0 [r-,r+]The Newtons sequence will converge to rSecant MethodFrom Algorithm:Input: f C1 [a,b], tolerance Initialization: r0, r1 in [a,b]While |r1-r0| > r2 r1 f(r1) r1-r0 / f(r1) f(r0)r0 r1r1 r2Order of Convergence (of iterative methods)Assume

Review from student

Studypool Student
" The best tutor out there!!!! "
Ask your homework questions. Receive quality answers!

Type your question here (or upload an image)

1820 tutors are online

Brown University





1271 Tutors

California Institute of Technology




2131 Tutors

Carnegie Mellon University




982 Tutors

Columbia University





1256 Tutors

Dartmouth University





2113 Tutors

Emory University





2279 Tutors

Harvard University





599 Tutors

Massachusetts Institute of Technology



2319 Tutors

New York University





1645 Tutors

Notre Dam University





1911 Tutors

Oklahoma University





2122 Tutors

Pennsylvania State University





932 Tutors

Princeton University





1211 Tutors

Stanford University





983 Tutors

University of California





1282 Tutors

Oxford University





123 Tutors

Yale University





2325 Tutors