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- W176817962 abstract "This chapter discusses the solution of equations of low orders and extraction of roots. In solving equations of general form, use of Newton's method is possible when an approximate value of a root is known, and then the process may diverge if the approximate value is not sufficiently close to the one being sought. In extraction of roots it is sufficient that the original approximation has the same sign as the unknown value of the root. Therefore, Newton's method may be applied not only for making more accurate the value of a root found by another method, but as an independent method, allowing all the calculations to be carried out from beginning to end. Iteration with quadratic convergence is roughly equivalent to Newton's method in speed of convergence, but no division has to be carried out. The calculational scheme is almost as simple as in the method of iteration. The method of iteration in view of the comparatively slow convergence, requires a large quantity of calculations, but allows division to be avoided." @default.
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- W176817962 date "1961-01-01" @default.
- W176817962 modified "2023-09-27" @default.
- W176817962 title "SOLUTION OF EQUATIONS OF LOW ORDERS AND EXTRACTION OF ROOTS" @default.
- W176817962 doi "https://doi.org/10.1016/b978-1-4832-0064-4.50011-7" @default.
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