第一章 单元测试
1、判断题：When the error propagation formula is 
, it is called exponential error propagation. ( )
A:对
B:错
正确答案:【错】
2、单选题：When performing（）operation with two similar numbers, it is easy to cause larger errors.（
A:Subtraction
B:Addition
C:Multiplication
D:Division
正确答案:【Subtraction】
3、多选题：Which problems should be solved by numerical analytical tool ( )?
A:
B:
C:
D:
正确答案:【
;
】
4、单选题：If p* =10.001 is an approximate of p = 10.000, then the relative error is ( )
A:
B:
C:
D:
正确答案:【
】
5、单选题：To approach 1/3, we should use at least ( ) significant digits to guarantee a relative error of 
A:
B:
C:
D:
正确答案:【
】
第二章 单元测试
1、判断题：Suppose 
is a sequence that converges to p, with 
for all n. If positive constants 
and 
exist with
.
Then, if 
, the sequence is linearly convergent. ( )
A:错
B:对
正确答案:【对】
2、单选题：The convergence rate of the bisection method is（）.
A:
B:
C:
D:
正确答案:【
】
3、单选题：The convergence rate of the Newton’s method is（）.
A:
B:
C:
D:
正确答案:【
】
4、判断题：Let 
and 
. Use Newton’s method to find 
. 
can be used as an initial point? （）
A:对
B:错
正确答案:【错】
5、判断题：The fixed-point problem g(x)=x-x3-4×2+10 cannot converge for initial point x0=1.5. （）
A:错
B:对
正确答案:【对】
第三章 单元测试
1、判断题：If a vector sequence converges to X in the L1 norm, it also converges to X in the 
norm.（）
A:错
B:对
正确答案:【对】
2、判断题：A sufficient condition for the existence of a unique fixed point is within a given interval 
.（）
A:错
B:对
正确答案:【错】
3、判断题：When the initial value is incorrectly selected, both fixed-point iteration and Newton’s method will fail to converge.（）
A:对
B:错
正确答案:【对】
4、判断题：Beginning with 
, the second iteration of Newton’s method for the equation 
is 
0.6860. ( )
A:对
B:错
正确答案:【对】
5、单选题：The convergence rate of the fixed-point iterative method is（）.
A:
B:
C:
D:
正确答案:【
】
第四章 单元测试
1、判断题：If A is symmetric, then 
. （）
A:错
B:对
正确答案:【对】
2、判断题：Given the linear system
The Gauss-Seidel algorithm can be used to solve the system. ( )
A:对
B:错
正确答案:【对】
3、判断题：If the spectral radius 
of a matrix A satisfies 
, then A is a convergent matrix. ( )
A:对
B:错
正确答案:【对】
4、多选题：The iterative calculation formula for linear problems is 
, the iterative process can converge when T satisfies which of the following conditions?（）
A:n is large enough, the L1 norm of 
is small enough
B:T is a convergent matrix
C:The spectral radius of T is less than 1.
D:n is large enough, the L2 norm of 
is small enough
正确答案:【n is large enough, the L1 norm of is small enough
;
T is a convergent matrix
;
The spectral radius of T is less than 1.
;
n is large enough, the L2 norm of is small enough
】
5、判断题：For the iterative solution of linear problems, the Jacobi algorithm always converge faster than the Gauss-Seidel algorithm.（）
A:对
B:错
正确答案:【错】
第五章 单元测试
1、判断题：Passing n points, a polynomial with degree no more than n that satisfies the interpolation conditions exists and is unique.（）
A:错
B:对
正确答案:【错】
2、多选题：Which of the following statements are correct about polynomial fitting?（）
A:One of the advantages of polynomial fitting is that the algebraic operations of polynomials are still polynomials
B:The polynomial with the highest degree n-1 which pass through n given points is unique
C:Taylor polynomials can only approximate a function at a certain point
D:In a closed interval, there is no polynomial function to approximate the exponential function with sufficient precision
正确答案:【One of the advantages of polynomial fitting is that the algebraic operations of polynomials are still polynomials;
The polynomial with the highest degree n-1 which pass through n given points is unique;
Taylor polynomials can only approximate a function at a certain point】
3、判断题：Let 
be the interpolation polynomial for the data(0,0),(0.5,y),(1,3),and(2,2).The coefficient of 
in is 6. Then y = 4.25. ( )
A:错
B:对
正确答案:【对】
4、判断题：Construct the Lagrange interpolating polynomial of degree 2 for the given values of x and y:
Then y =6.712 when x = 4.8. ( )
A:对
B:错
正确答案:【对】
5、判断题：Write the linear Lagrange interpolating polynomial that passes through the points (2; 4) and (5; 1). Then f(7)={2}. ( )
A:错
B:对
正确答案:【错】
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