数值计算（国外英文资料）.docVIP

数值计算（国外英文资料） Problem solving Take 3.14, 3.15, as an approximation of PI, and find the absolute error, relative error, and number of valid digits. Analysis: the method of absolute error is calculated directly by definition. The general way to do this is to figure out the absolute error and then calculate it by definition. Notice that the relative error should not be asked for the absolute error. Valid number digits can be according to the definition, the first to be determined by the absolute error of approximate number of absolute error is less than half that of a unit, and then determine which one is the number of effective bottom, further determine the effective Numbers and effective digital. With the theorem 2, you can answer it more formally by theorem 2. According to theorem 2, the first step is to convert the Numbers into scientific notation and then solve them. Solution: (1) absolute error: E (x) = PI -3.14 = 3.. - 3.14 = 0.00159... Material of 0.0016. The relative error: Significant figures: Because PI is 3.. = 0.314159265... Times 10, 3.14 is 0.314 times 10, and m is 1. PI -3.14 = 3.. - 3.14 = 0.00159... So │ │ PI - 3.14 = 3.14... Its less than or equal to 0.005 = 0.5 times 10 minus 2 So, 3.14 has three valid digits as an approximation of PI. (2) absolute error: E (x) = PI -3.15 = 3.. -3.14 = -0.008407... Material - 0.0085. The relative error: Significant figures: Because PI is 3.. = 0.314159265... Times 10, 3.15 is 0.315 times 10, and m is equal to 1. PI -3.15 = 3.. -3.15 = -0.008407... So │ │ PI - 3.15 = 3.15... Its less than 0.05, which is 0.5 times 10 minus 1 So, the approximate value of 3.15 as PI is two valid digits. (3) absolute error: The relative error: Significant figures: Because PI is 3.. = 0.314159265... X 10, , m = 1. while so So, there are three valid digits for the approximate value of PI. (4) absolute error: The relative error: Significant figures: Because PI is 3.1415926