Math 510: Numerical Methods for Linear Algebra - Revision history

Ls5: /* Catalog Information */

2019-11-14T16:58:51Z

‎Catalog Information

Ls5: /* Prerequisite */

2013-09-05T21:39:05Z

‎Prerequisite

Ls5: /* Prerequisite */

2013-09-05T21:38:44Z

‎Prerequisite

Ls5: /* Prerequisite */

2013-09-05T21:38:17Z

‎Prerequisite

Ls5: moved Math 510 to Math 510: Numerical Methods for Linear Algebra

2013-04-03T22:37:39Z

moved Math 510 to Math 510: Numerical Methods for Linear Algebra

Roundy at 20:19, 10 May 2012

2012-05-10T20:19:51Z

Roundy at 20:14, 10 May 2012

2012-05-10T20:14:02Z

Sc96: /* Desired Learning Outcomes */

2010-10-19T19:33:21Z

‎Desired Learning Outcomes

Sc96: /* Minimal learning outcomes */

2010-10-19T19:19:53Z

‎Minimal learning outcomes

Sc96: /* Minimal learning outcomes */

2010-10-19T19:18:18Z

‎Minimal learning outcomes

Show changes

← Older revision		Revision as of 16:58, 14 November 2019
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	=== Credit Hours ===		=== Credit Hours ===
	3		3
		+
		+	=== Offered ===
		+	F

	=== Prerequisite ===		=== Prerequisite ===

@@ Line 8: / Line 8: @@
 === Prerequisite ===
-[[Math 314]], [[CS 142]]; or equivalent.
+[[Math 314]], CS 142; or equivalent.
 === Description ===

@@ Line 8: / Line 8: @@
 === Prerequisite ===
-[[Math 314]], [[Math 410|410]]; or equivalents.
+[[Math 314]], [[CS 142]]; or equivalent.
 === Description ===

@@ Line 8: / Line 8: @@
 === Prerequisite ===
-[[Math 343]], [[Math 410|410]]; or equivalents.
+[[Math 314]], [[Math 410|410]]; or equivalents.
 === Description ===

← Older revision		Revision as of 20:19, 10 May 2012
Line 6:		Line 6:
	=== Credit Hours ===		=== Credit Hours ===
	3		3
−
−	~~=== Offered ===~~
−	~~Fall~~

	=== Prerequisite ===		=== Prerequisite ===

← Older revision	Revision as of 22:37, 3 April 2013
(No difference)

← Older revision		Revision as of 20:14, 10 May 2012
Line 6:		Line 6:
	=== Credit Hours ===		=== Credit Hours ===
	3		3
		+
		+	=== Offered ===
		+	Fall

	=== Prerequisite ===		=== Prerequisite ===

← Older revision		Revision as of 19:33, 19 October 2010
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	== Desired Learning Outcomes ==		== Desired Learning Outcomes ==
		+
		+	This course is designed to prepare students to solve linear algebra
		+	problems arising from many applications such as mathematical models of physical or engineering processes.
		+	Students are introduced to modern concepts and methodologies in numerical linear algebra, with particular emphasis on t
		+	methods that can be used to solve very large scale problems. In depth discussion of
		+	theoretical aspects such as stability and convergence
		+	will be used to enhance the students' understanding of the
		+	numerical methods. Students will also be required to perform some
		+	programming and computation so as to gain experience in
		+	implementing and observing the numerical
		+	performance of the various numerical methods.
		+
		+	The course addresses the University goal of developing the skills
		+	of sound thinking, effective communication and quantitative
		+	reasoning. The course also allow students, especially
		+	undergraduate students, to develop some depth and consequently
		+	competence in an important area of applied mathematics.
		+
		+	This course requires knowledge of higher level courses in
		+	mathematics. The course also serves as an introductory graduate
		+	level course to prepare the students to apply the methods learned
		+	in their research projects.

	=== Prerequisites ===		=== Prerequisites ===

@@ Line 26: / Line 26: @@
 Know properties of unitary matrices
 Know general and practical definitions and properties of norms
 Know definition and properties of SVD
 Know definitions of and properties of projectors and orthogonal projectors
 Be able to state and apply  classical Gram-Schmidt and modified Gram-Schmidt algorithms
 Know definition and properties of a Householder reflector
 Know how to construct Householder QR factorization
 Know how least squares problems arise from a polynomial fitting problem
 Know how to solve least square problems using
    (1) normal equations/pseudoinverse,
    (2) QR factorization and
    (3) SVD
 Be able to define the condition of a problem and related condition number
 Know how to calculate the condition number of a matrix
 Understand the concepts of well-conditioned and ill-conditioned problems
-Know how to derive the conditioning bound of matrix-vector multiplication/ linear system solve
-Be able to state the precise definition of stability and backward stability
+Know how to derive the conditioning bounds
 Be able to apply the fundamental axiom of floating point arithmetic to determine stability
 Know the difference between stability and conditioning
 Know the four condition numbers of a least squares problem
 Know how to construct LU  and PLU factorizations
 Know how PLU is related to Gaussian elimination
 Understand Cholesky decomposition
 Know properties of eigenvalues and eigenvectors under similarity transformation and shift
 Know various matrix decomposition related to eigenvalue calculation:
    (1) spectral decomposition
@@ Line 54: / Line 74: @@
    (2) Schur decomposition
 Understand why and how matrices can be reduced to Hessenberg form
 Know various form of power method and what Rayleigh quotient iteration and their properties and convergence rates
 Know the QR algorithm with shifts
 Understand simultaneous iteration and QR algorithm are mathematically equivalent
 Understand the  Arnoldi algorithm and its properties
 Know the polynomial approximation problem associated with Arnoldi method
 Be able to state the GMRES algorithm
 Be able to state three term recurrence of Lanczos iteration for real symmetric matrices
 Understand the CG algorithm and its properties
 Know the v-cycle multigrid algorithm and the full multigrid algorithm
 Know how to construct  preconditioners: (block) diagonal, incomplete LU and incomplete Cholesky preconditioners
 Know CGN and BCG and other Krylov space methods