Let A be an nx n nonsingular matrix. (a) Find the number of arithmetic operations for the LU factorization, which is based on the Gaussian elimination with partial pivoting. [Note: To compare two numbers, say, a and b, we need to perform the subtraction a - b and then check the sign of the result. So, finding the maximum of k numbers, requires k-1 subtractions.] (b) Find the number of arithmetic operations required to find the inverse matrix A-¹ using the LU factorization from part (a). [Note: The LU factorization needs to be performed only once.] (c) Suppose that A-¹ has been calculated. Find the number of arithmetic operations required to compute the multiplication A-¹b.
Let A be an nx n nonsingular matrix. (a) Find the number of arithmetic operations for the LU factorization, which is based on the Gaussian elimination with partial pivoting. [Note: To compare two numbers, say, a and b, we need to perform the subtraction a - b and then check the sign of the result. So, finding the maximum of k numbers, requires k-1 subtractions.] (b) Find the number of arithmetic operations required to find the inverse matrix A-¹ using the LU factorization from part (a). [Note: The LU factorization needs to be performed only once.] (c) Suppose that A-¹ has been calculated. Find the number of arithmetic operations required to compute the multiplication A-¹b.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Let A be an n x n nonsingular matrix.
(a) Find the number of arithmetic operations for the LU factorization, which is based on the
Gaussian elimination with partial pivoting. [Note: To compare two numbers, say, a and b,
we need to perform the subtraction a - b and then check the sign of the result. So, finding
the maximum of k numbers, requires k – 1 subtractions.]
(b) Find the number of arithmetic operations required to find the inverse matrix A-¹ using the
LU factorization from part (a). [Note: The LU factorization needs to be performed only
once.]
(c) Suppose that A-¹ has been calculated. Find the number of arithmetic operations required
to compute the multiplication A-¹b.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F91f76606-a4d9-42f0-be0d-7b1366a5593f%2F3f0ad61f-c421-43fc-b57e-3a0fa15456e7%2F9gnxl2j_processed.png&w=3840&q=75)
Transcribed Image Text:Let A be an n x n nonsingular matrix.
(a) Find the number of arithmetic operations for the LU factorization, which is based on the
Gaussian elimination with partial pivoting. [Note: To compare two numbers, say, a and b,
we need to perform the subtraction a - b and then check the sign of the result. So, finding
the maximum of k numbers, requires k – 1 subtractions.]
(b) Find the number of arithmetic operations required to find the inverse matrix A-¹ using the
LU factorization from part (a). [Note: The LU factorization needs to be performed only
once.]
(c) Suppose that A-¹ has been calculated. Find the number of arithmetic operations required
to compute the multiplication A-¹b.
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