Analyse Numerique Matricielle DEA d'analyse numerique by Despres B.

By Despres B.

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2) It is possible to formulate algorithms which can handle class of similar problems. For example, algorithms to solve polynomial equations of degree n may be written. (3) Rounding errors are negligible as compared to methods based on closed form solutions. 3 ORDER (OR RATE) OF CONVERGENCE OF ITERATIVE METHODS Convergence of an iterative method is judged by the order at which the error between successive approximations to the root decreases. The order of convergence of an iterative method is said to be kth order convergent if k is the largest positive real number such that lim i →∞ ei +1 e k i ≤A Where A, is a non-zero finite number called asymptotic error constant and it depends on derivative of f(x) at an approximate root x.

Example 28. The percentage error in R which is given by R = Sol. 505. 20 11 11 Example 29. 8 cm and 45° respectively. Find the possible error in the area of a triangle if the error in sides is correct to a millimeter and the angle is measured correct to one degree. Sol. 539 sq. cm. 4142135 17 ERRORS AND FLOATING POINT Example 30. 5%. How accurately the radius should be measured. Sol. 25. 4 Example 31. 1%. How accurately should the diameter be measured? = Sol. Let d is the diameter of a circle, and then its area is given by A = πd 2 .

4142135 17 ERRORS AND FLOATING POINT Example 30. 5%. How accurately the radius should be measured. Sol. 25. 4 Example 31. 1%. How accurately should the diameter be measured? = Sol. Let d is the diameter of a circle, and then its area is given by A = πd 2 . 05 · πd 4d 2 Example 32. 5 cm and A = 45o, find allowable errors in b, c, and A such that the area of ∆ABC may be determined nearest to a square centimeter. Sol. 055 cm. 049 cm. 006 radians. 5 × 3 2 2 2 ∂A Example 33. 7 cm and ∠ B = 90o. If possible errors in the computed value of b and a are 2 mm and 1 mm respectively, find the possible error in the measurement of angle A.

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