課程名稱︰數值方法
課程性質︰計算機運算處理
課程教師︰林智仁
開課學院：電機資訊學院
開課系所︰資工所
考試日期（年月日）︰100/3/29
考試時限（分鐘）：120
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
-Please give details of your calculation. A direct answer without
explanation is not counted.
-Your answers must be in English
Problem 1 (15%)
What is the bit string of -37 under IEEE 754 standard? We assume single
precision. Please explain details instead of just giving a string.
Problem 2 (30%)
Consider the following martix:
[ 1 4 7 ]
A = [ 2 5 8 ]
[ 3 6 10 ]
We would like to find the LU factorization using the pivoting
(a) Give all details of finding
M P ...M P A = U
n-1 n-1 1 1
(b) Find P such that
PA = LU (1)
where L and U are lower- and upper-triangular matrices, respectively.
(c) If we solve the linear system
[ 6 ]
Ax = b = [ 9 ]
[ 12]
show how to use (1) to solve the linear system
Problem 3 (20%)
Consider the following matrix:
[16 8 4 12]
A = [8 8 0 2 ]
[4 0 27 0 ]
[12 2 0 30]
Generate the Cholesky factorization using the outer product form.
Problem 4 (20%)
In exact arithmetic, the addition operation is commutative, i.e.,
x + y = y + x
for any two numbers x, y and also associative, i.e.,
x + (y + z) = (x + y) + z
for any x, y and z. Is the floating point addition operation commutative?
Is it associative? We assume exact rounded operations.
Problem 5 (15%)
What is the smallest positive denomalized number under the IEEE standard
(single precision)?
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