Newton iteration method: Newton iteration method is a numerical solution method based on Taylor series expansion, which approximates the real value through continuous iteration. The basic idea is to use the tangent of a function at a certain point to approximate the curve of the function near that point. Newton iteration method has fast convergence speed and high accuracy, but it needs to calculate the derivative of the function.
2. Dichotomy: Dichotomy is a simple and intuitive method to find the square root. By continuously dividing the search interval into two parts, the search range is gradually narrowed until a solution that meets the accuracy requirements is found. The advantage of dichotomy is that it is simple to implement, but its convergence speed is slow, which may require more iterations.
3. Babylonian method: Babylonian method is a method to solve the square root based on algebraic principle. By constantly adding, subtracting, multiplying and dividing the number to be solved and the known number, it gradually approaches the true value. The advantage of Babylonian method is that it can handle negative numbers and non-integers, but it is more complicated to implement.
4. Look-up table method: Look-up table method is a method to calculate the square root value in a certain range in advance, and then directly find the corresponding result according to the input value. The advantage of look-up table method is fast calculation, but it needs to occupy a large storage space.
Square root meaning
1, the square root, also called quadratic square root, is the original value obtained by squaring a number. For any real number, the square root exists. The significance of square root is that it provides a simple and intuitive way to express and solve problems related to area and quantity.
2. Square root is very important to express the relationship between area and quantity. For example, if the side length of a square is a, its area is A 2. Through the square root, we can easily convert the side length of a square into an area, or convert the area into a side length. This transformation relationship is widely used in geometry and physics.
3. Square root has many applications in solving practical problems. In physics, the square root is often used to calculate the action of force. Through the square root, we can easily convert the magnitude of force into the magnitude of acceleration, thus better reflecting the state of geographical movement. Square root also plays an important role in mathematics. We can convert some complicated equations into simple ones.