3.1 (12/25) LU decomposition Perform LU decomposition on matrix A by implementing your own function (lu) based on following pseudocode. Please validate your final solution by using e = ||LU – PA||F, which should be a small value (for this problem, e < 10-6). Algorithm 1 LU Decomposition with Partial Pivoting DI is the identity matrix Dn is the number of rows of A Input: U + A, L + I, P + I 1: for k = 1:n – 1 do Find i > k to maximize |U(i, k)| U(k, k : n) + U(i, k : n) L(k, 1 : k) → L(i, 1 : k) P(k,:) + P(i, :) for j = k +1: n do L(j, k) = U (j, k)/U(k, k) U(j, k : n) = U(j, k : n) – L(j, k)U(k, k : n) end for %3D 2: D switching specified elements 3: 4: 5: 6: 7: 8: 9: 10: end for 11: return P, L,U

3.1 (12/25) LU decomposition Perform LU decomposition on matrix A by implementing your own function (lu) based on following pseudocode. Please validate your final solution by using e = ||LU – PA||F, which should be a small value (for this problem, e < 10-6). Algorithm 1 LU Decomposition with Partial Pivoting DI is the identity matrix Dn is the number of rows of A Input: U + A, L + I, P + I 1: for k = 1:n – 1 do Find i > k to maximize |U(i, k)| U(k, k : n) + U(i, k : n) L(k, 1 : k) → L(i, 1 : k) P(k,:) + P(i, :) for j = k +1: n do L(j, k) = U (j, k)/U(k, k) U(j, k : n) = U(j, k : n) – L(j, k)U(k, k : n) end for %3D 2: D switching specified elements 3: 4: 5: 6: 7: 8: 9: 10: end for 11: return P, L,U

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

3.1 (12/25) LU decomposition Perform LU decomposition on matrix A by implementing your
own function (lu) based on following pseudocode. Please validate your final solution by using
||LU – PA||F, which should be a small value (for this problem, e < 10-6).
Algorithm 1 LU Decomposition with Partial Pivoting
Input: U + A, L + I, P + I
DI is the identity matrix
1: for k = 1:n – 1 do
Find i > k to maximize |U(i, k)|
U(k, k : n) + U (i, k : n)
L(k, 1: k) + L(i, 1 : k)
P(k, :) + P(i, :)
for j = k +1:n do
L(j, k) = U (j, k)/U(k, k)
U(j, k : n) = U(j, k : n) – L(j, k)U(k, k : n)
end for
Dn is the number of rows of A
-
2:
3:
D switching specified elements
4:
5:
6:
7:
8:
9:
10: end for
11: return P, L,U

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