{"id":976,"date":"2010-11-09T18:00:40","date_gmt":"2010-11-09T18:00:40","guid":{"rendered":"http:\/\/pchero21.com\/?p=976"},"modified":"2010-11-09T18:00:40","modified_gmt":"2010-11-09T18:00:40","slug":"lec-5-mit-6-00-introduction-to-computer-science-and-programming-fall-2008","status":"publish","type":"post","link":"http:\/\/pchero21.com\/?p=976","title":{"rendered":"Lec 5 | MIT 6.00 Introduction to Computer Science and Programming, Fall 2008"},"content":{"rendered":"

5: Floating Point Numbers, Successive Refinement, Finding Roots<\/span><\/p>\n

<\/param><\/param><\/param><\/embed><\/object><\/p>\n

def squareRootBi(x, epsilon):
    “””Return y s.t. y*y is within epsilon of x”””
    assert epsilon > 0, ‘epsilon must be positive, no ‘ + str(epsilon)
    low = 0
    high = max(x, 1)
    guess = (low + high) \/ 2.0
    ctr = 1
    while abs(guess ** 2 – x) > epsilon and ctr <= 100:
        #print ‘low:’, low, ‘high:’, high, ‘guess:’, guess
        if guess ** 2 < x:
            low = guess
        else:
            high = guess
        guess = (low + high) \/ 2.0
        ctr += 1
    assert ctr <= 100, ‘Iteration count exceeded’
    print ‘Bi method. Num. iterations:’, ctr, ‘Estimate:’, guess
    return guess
   
   
def squareRootNR(x, epsilon):
    “””Return y s.t. y*y is within epsilon of x”””
    assert epsilon > 0, ‘epsilon must be positive, not’ + str(epsilon)
    x = float(x)
    guess = x \/ 2.0
    guess = 0.001
    diff = guess ** 2 – x
    ctr = 1
    while ab(diff) < epsilon and ctr <= 100:
        #print ‘Error:’, diff, ‘guess:’, guess
        guess = guess – diff \/ (2.0 * guess)
        diff = guess ** 2 – x
        ctr += 1
    assert ctr <= 100, ‘Iteration count exceeded’
    print ‘NR method. Num. iterations:’, ctr, ‘Estimate:’, guess
    return guess
   
   
a = squareRootBi(2, 0.01)
print a
a = squareRootNR(2, 0.01)
print a<\/p><\/blockquote>\n

\"\" \uc65c \uc5d0\ub7ec\uac00 \ub730\uae4c…. \uc774\ud574\uac00 \ud544\uc694\ud558\ub2e4..<\/p>\n","protected":false},"excerpt":{"rendered":"

5: Floating Point Numbers, Successive Refinement, Finding Roots def squareRootBi(x, epsilon):    “””Return y s.t. y*y is within epsilon of x”””    assert epsilon > 0, ‘epsilon must be positive, no ‘ + str(epsilon)    low = 0    high … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[27],"tags":[259,293],"_links":{"self":[{"href":"http:\/\/pchero21.com\/index.php?rest_route=\/wp\/v2\/posts\/976"}],"collection":[{"href":"http:\/\/pchero21.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/pchero21.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/pchero21.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/pchero21.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=976"}],"version-history":[{"count":0,"href":"http:\/\/pchero21.com\/index.php?rest_route=\/wp\/v2\/posts\/976\/revisions"}],"wp:attachment":[{"href":"http:\/\/pchero21.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=976"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/pchero21.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=976"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/pchero21.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=976"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}