CSE/MATH 6643: Numerical Linear Algebra
Haesun Park
[email protected]
School of Computational Science and Engineering
College of Computing
Georgia Institute of Technology
Atlanta, GA 30332, USA
Lecture 8
QR Factorization
6
QR Factorization
For solving L
CSE/MATH 6643: Numerical Linear Algebra
Haesun Park
[email protected]
School of Computational Science and Engineering
College of Computing
Georgia Institute of Technology
Atlanta, GA 30332, USA
Lecture 12
Classical Gram-Schmidt (CGS) for Reduced QRD
Giv
CSE/MATH 6643: Numerical Linear Algebra
Haesun Park
[email protected]
School of Computational Science and Engineering
College of Computing
Georgia Institute of Technology
Atlanta, GA 30332, USA
Lecture 18
Eigenvalue Problem
Symmetric Eigenvalue Decompos
CSE6643/MATH6643, Numerical Linear Algebra, Spring 2014
Mon. Wed. 3:05-4:25 pm
Instr Center 105, Prof. Haesun Park
Prerequisites: Introductory Numerical Analysis and Linear Algebra background, or Permission of the
instructor.
Instructors Oce Hours: Mon. 2
HW 2 Solutions
March 3, 2014
1
The information in the question implies that
A + ei eT
j
(1)
is non-singular for all = 0. From the Sherman-Morrison-Woodbury formula we have the condition
1 + eT A1 ei = 0 R, = 0
j
which, in turn implies that (A
1
(2)
)ij =
HW 1 Solutions
February 24, 2014
1
A + iB = (CE DF ) + i (DE + CF ) .
(1)
W = CE + DE CF DF.
(2)
Also,
Now, note that A = W + CF DE , and B = DE + CF . Thus the three multiplications required for computing A and B are CF , DF , and W = (C + D) (E F ).
2
U
Math 6643, Numerical Linear Algebra
HW 1, Due on Wednesday, September 20
Notice: For the computational problems, you must design your own ways, such as using
tables and plots etc, to present the results you obtain. And you must show the procedure
you take
Math 6643, Numerical Linear Algebra
HW 2, Due on Wednesday, October 11
Notice: For the computational problems, you must design your own ways, such as using
tables and plots etc, to present the results you obtain. And you must show the procedure
you take,
CSE/MATH 6643: Numerical Linear Algebra
Haesun Park
[email protected]
School of Computational Science and Engineering
College of Computing
Georgia Institute of Technology
Atlanta, GA 30332, USA
Lecture 15
Least Square Problem Rank Deficient
Computin
MATH 6643, Test on basic knowledge of linear algebra
not for grading
Name:
, GTID:
Please do not use calculators, books and notes during the test.
TEST TIME: 25 Minutes
Problem 1 Find a linear function that fits the four data points (1, 8),
(0, 8), (1, 4)
CSE/MATH 6643: Numerical Linear Algebra
Haesun Park
[email protected]
School of Computational Science and Engineering
College of Computing
Georgia Institute of Technology
Atlanta, GA 30332, USA
Lecture 10
QR Factorization
Problem: Given a vector x,
8/20/2017
Math6643 Course Web Page, Fall 2017
Numerical Linear Algebra
Math 6643, Fall, 2017
Mondays and Wednesdays, 3:00-4:15 p.m. in Klaus 2447
Instructor: Haomin Zhou (email: [email protected])
Ofce Hours: Mondays and Wednesdays., 4:15 p.m. - 5:15
CSE/MATH 6643: Numerical Linear Algebra
Haesun Park
[email protected]
School of Computational Science and Engineering
College of Computing
Georgia Institute of Technology
Atlanta, GA 30332, USA
Lecture 7
Cholesky Decomposition and Banded Systems
Definit
CSE/MATH 6643: Numerical Linear Algebra
Haesun Park
[email protected]
School of Computational Science and Engineering
College of Computing
Georgia Institute of Technology
Atlanta, GA 30332, USA
Lecture 1
What is Numerical Analysis?
Three great branc
CSE/MATH 6643: Numerical Linear Algebra
Haesun Park
[email protected]
School of Computational Science and Engineering
College of Computing
Georgia Institute of Technology
Atlanta, GA 30332, USA
Lecture 6
Symmetric Positive Denite Matrix & Cholesky
Decom
CSE/MATH 6643: Numerical Linear Algebra
Haesun Park
[email protected]
School of Computational Science and Engineering
College of Computing
Georgia Institute of Technology
Atlanta, GA 30332, USA
Lecture 11
Least Squares Problem Full Rank
Least Square
CSE/MATH 6643, Spring 2016
HW1 Solutions
1
P1.1.1, page 13
v = A(:, 1)
v(1) = v(1) xr
for i = r 1 : 1 : 1 do
v = Av xi v
end for
After the algorithm v would be the rst column of M . The complexity of this algorithm is 1 + (r 1)(2n2
n + 2n) = O(rn2 ) ops.
CSE/MATH 6643: Numerical Linear Algebra
Haesun Park
[email protected]
School of Computational Science and Engineering
College of Computing
Georgia Institute of Technology
Atlanta, GA 30332, USA
Lecture 5
LU Factorization
Applications of P A = LU
Lin
CSE/MATH 6643: Numerical Linear Algebra
Haesun Park
[email protected]
School of Computational Science and Engineering
College of Computing
Georgia Institute of Technology
Atlanta, GA 30332, USA
Lecture 4
LU Factorization
G.E. with Partial Pivoting
1
CSE/MATH 6643: Numerical Linear Algebra
Haesun Park
[email protected]
School of Computational Science and Engineering
College of Computing
Georgia Institute of Technology
Atlanta, GA 30332, USA
Lecture 2
Introduction
Introduction
Topics
1. Linear sy
CSE/MATH 6643: Numerical Linear Algebra
Haesun Park
[email protected]
School of Computational Science and Engineering
College of Computing
Georgia Institute of Technology
Atlanta, GA 30332, USA
Lecture 3
LU Factorization
LU Factorization
How to find
CSE/MATH 6643: Numerical Linear Algebra
Haesun Park
[email protected]
School of Computational Science and Engineering
College of Computing
Georgia Institute of Technology
Atlanta, GA 30332, USA
Lecture 9
QR Factorization
In general, we need to nd Ho
CSE/MATH 6643: Numerical Linear Algebra
Haesun Park
[email protected]
School of Computational Science and Engineering
College of Computing
Georgia Institute of Technology
Atlanta, GA 30332, USA
Lecture 8
QR Factorization
QR Factorization
For solving
CSE6643/MATH6643:Numerical Linear Algebra
Haesun Park
[email protected]
School of Computational Science and Engineering
College of Computing
Georgia Institute of Technology
Atlanta, GA 30332, USA
Lecture 2
Introduction
1
1.1
Introduction
Topics
1. Linea
CSE/MATH 6643: Numerical Linear Algebra
Haesun Park
[email protected]
School of Computational Science and Engineering
College of Computing
Georgia Institute of Technology
Atlanta, GA 30332, USA
Lecture 11
Least Squares Problem Full Rank
7 Least Squa
CSE/MATH 6643: Numerical Linear Algebra
Haesun Park
[email protected]
School of Computational Science and Engineering
College of Computing
Georgia Institute of Technology
Atlanta, GA 30332, USA
Lecture 12
Classical Gram-Schmidt (CGS) for Reduced QRD
CSE/MATH 6643: Numerical Linear Algebra
Haesun Park
[email protected]
School of Computational Science and Engineering
College of Computing
Georgia Institute of Technology
Atlanta, GA 30332, USA
Lecture 13
Least Squares Problem
7.4
Solved by Singular Val
CSE/MATH 6643: Numerical Linear Algebra
Haesun Park
[email protected]
School of Computational Science and Engineering
College of Computing
Georgia Institute of Technology
Atlanta, GA 30332, USA
Lecture 19
Eigenvalue Problem - Numerical Methods
I
Hne
CSE/MATH 6643: Numerical Linear Algebra
Haesun Park
[email protected]
School of Computational Science and Engineering
College of Computing
Georgia Institute of Technology
Atlanta, GA 30332, USA
Lecture 6
Symmetric Positive Definite & Cholesky Decomp
CSE/MATH 6643: Numerical Linear Algebra
Haesun Park
[email protected]
School of Computational Science and Engineering
College of Computing
Georgia Institute of Technology
Atlanta, GA 30332, USA
Lecture 5
LU Factorization
3.9 Applications of P A
= LU
CSE/MATH 6643: Numerical Linear Algebra
Haesun Park
[email protected]
School of Computational Science and Engineering
College of Computing
Georgia Institute of Technology
Atlanta, GA 30332, USA
Lecture 8
QR Factorization
6 QR Factorization
For solvi
CSE/MATH 6643: Numerical Linear Algebra
Haesun Park
[email protected]
School of Computational Science and Engineering
College of Computing
Georgia Institute of Technology
Atlanta, GA 30332, USA
Lecture 7
Symmetric Positive Definite & Cholesky Decomp