The arithmetic-geometric mean of two positive real numbers and y is defined in the following way....
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The arithmetic-geometric mean of two positive real numbers and y is defined in the following way. We define two sequences an and gn by ao = x, go = y, and for n > 0, an+1 = (an + gn)/2 Gn+1 = an In It is a theorem that the sequences (an) and (gn) tend to the same limit as n . This limit is called the arithmetic-geometric mean of x and y and written AGM (x, y). Write a function agm_sequences (x, y, k) which returns a list [a, g] where a = [a0, al, a2, ak] is the list of the first k + 1 terms of the sequence (an) with ao = x, of the sequence (gn) with go = y. and For example, if x [[1, 1, 1, 1], [1, 1, 1, 1]] = y 1 then an = - 1 and gn = 1 for all n, so agm_sequences (1, 1, 3) must return - = 2,90 = 8, a = 5,9 = 4 so agm_sequences (2, 8, 1) must return and if x = 2, y = 8 then ao [[2, 5], [8, 4]] (you may see 5.0 and 4.0 instead of 5 and 4 that's OK). g = [g0, g1, g2, gk] is the list of the first k + 1 terms The arithmetic-geometric mean of two positive real numbers and y is defined in the following way. We define two sequences an and gn by ao = x, go = y, and for n > 0, an+1 = (an + gn)/2 Gn+1 = an In It is a theorem that the sequences (an) and (gn) tend to the same limit as n . This limit is called the arithmetic-geometric mean of x and y and written AGM (x, y). Write a function agm_sequences (x, y, k) which returns a list [a, g] where a = [a0, al, a2, ak] is the list of the first k + 1 terms of the sequence (an) with ao = x, of the sequence (gn) with go = y. and For example, if x [[1, 1, 1, 1], [1, 1, 1, 1]] = y 1 then an = - 1 and gn = 1 for all n, so agm_sequences (1, 1, 3) must return - = 2,90 = 8, a = 5,9 = 4 so agm_sequences (2, 8, 1) must return and if x = 2, y = 8 then ao [[2, 5], [8, 4]] (you may see 5.0 and 4.0 instead of 5 and 4 that's OK). g = [g0, g1, g2, gk] is the list of the first k + 1 terms
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Related Book For
Introduction to Algorithms
ISBN: 978-0262033848
3rd edition
Authors: Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest
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