“secant method”的概念、定义、翻译、参考文献-科学参考

secant method

Mathematics

Computer

An iterative method for finding a root of the nonlinear equation f(x) = 0. It is given by the formula
$\begin{array}{l} x_{n + 2} = x_{n + 1} - \\ (x_{n + 1} - x_{n}) [f (x_{n + 1}) / (f (x_{n + 1}) - f (x_{n}))] \\ n = 0, 1, 2, \dots \end{array}$
where x₀ and x₁ are given starting values. This formula is derived by replacing f(x) by a straight line based on the last two iterates. Convergence is ultimately less rapid than for Newton’s method, but it can be overall more efficient on some problems since derivatives are not required.

单词	secant method
释义	secant method Mathematics Given two successive approximations to a function’s root a, the secant method calculates where the secant through these two points The secant method meets the x-axis and uses this as the next approximation. So the iteration is given by $x_{n + 1} = x_{n} - \frac{(x_{n} - x_{n - 1})}{f (x_{n}) - f (x_{n - 1})} \times f (x_{n}) for n = 1, 2, 3, … .$ Computer An iterative method for finding a root of the nonlinear equation f(x) = 0. It is given by the formula $\begin{array}{l} x_{n + 2} = x_{n + 1} - \\ (x_{n + 1} - x_{n}) [f (x_{n + 1}) / (f (x_{n + 1}) - f (x_{n}))] \\ n = 0, 1, 2, \dots \end{array}$ where x₀ and x₁ are given starting values. This formula is derived by replacing f(x) by a straight line based on the last two iterates. Convergence is ultimately less rapid than for Newton’s method, but it can be overall more efficient on some problems since derivatives are not required.
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