The IBM Sequoia computer can operate at speeds in excess of 16 petaflops per second (1 petaflop = 1015 flops). Use Ta- ble 1 to estimate the time required to perform the following operations on an invertible 100,000 × 100,000 matrix A. (a) Execute the forward phase of Gauss-Jordan elimination. (b) Execute the backward phase of Gauss-Jordan elimina- tion. (c) LU-decomposition of A.
The IBM Sequoia computer can operate at speeds in excess of 16 petaflops per second (1 petaflop = 1015 flops). Use Ta- ble 1 to estimate the time required to perform the following operations on an invertible 100,000 × 100,000 matrix A. (a) Execute the forward phase of Gauss-Jordan elimination. (b) Execute the backward phase of Gauss-Jordan elimina- tion. (c) LU-decomposition of A.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.2: Guassian Elimination And Matrix Methods
Problem 84E: Explain the differences between Gaussian elimination and Gauss-Jordan elimination.
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![Table 1
Approximate Cost for an n x n Matrix A with Large n
Algorithm
Cost in Flops
Gauss-Jordan elimination (forward phase)
Gauss-Jordan elimination (backward phase) n?
LU-decomposition of A
Forward substitution to solve Ly = b
Backward substitution to solve Ux = y
A-' by reducing [A |I] to [! | A-']
* 2n3
Compute A-'b
* 2n
3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff854fa05-8493-448a-b846-ce3869618452%2F05b4ab9e-515a-4a1a-9623-7126226ad97d%2F9fn1w6d_processed.png&w=3840&q=75)
Transcribed Image Text:Table 1
Approximate Cost for an n x n Matrix A with Large n
Algorithm
Cost in Flops
Gauss-Jordan elimination (forward phase)
Gauss-Jordan elimination (backward phase) n?
LU-decomposition of A
Forward substitution to solve Ly = b
Backward substitution to solve Ux = y
A-' by reducing [A |I] to [! | A-']
* 2n3
Compute A-'b
* 2n
3
![4. The IBM Sequoia computer can operate at speeds in excess
of 16 petaflops per second (1 petaflop = 1015 flops). Use Ta-
ble 1 to estimate the time required to perform the following
operations on an invertible 100,000 × 100,000 matrix A.
(a) Execute the forward phase of Gauss-Jordan elimination.
(b) Execute the backward phase of Gauss-Jordan elimina-
tion.
(c) LU-decomposition of A.
(d) Find A-l by reducing [A | I] to [I | A¬'].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff854fa05-8493-448a-b846-ce3869618452%2F05b4ab9e-515a-4a1a-9623-7126226ad97d%2F39ksxf_processed.png&w=3840&q=75)
Transcribed Image Text:4. The IBM Sequoia computer can operate at speeds in excess
of 16 petaflops per second (1 petaflop = 1015 flops). Use Ta-
ble 1 to estimate the time required to perform the following
operations on an invertible 100,000 × 100,000 matrix A.
(a) Execute the forward phase of Gauss-Jordan elimination.
(b) Execute the backward phase of Gauss-Jordan elimina-
tion.
(c) LU-decomposition of A.
(d) Find A-l by reducing [A | I] to [I | A¬'].
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