### Study Questions Homework 6 (pdf) has questions related to solving nonlinear equations.

### Graded Homework 4 (pdf).

### Graded Homework 3 (pdf).

### Study Questions Homework 5 (pdf) has questions related to steepest descent, conjugate direction-based iterative methods and CG for SPD matrices and the associated linear systems.

### Study Questions Homework 4 (pdf) is a set of problems related to stationary iterative methods for linear systems. The problems contain proofs of some of the important theorems stated in Sets 10 and 11 of the lecture notes. They are given in increasing level of sophistication and present particular ways of proving the fundamental theorems. You are responsible for the results stated in the theorems in this problem set and in the lecture notes but the more sophisticated and detailed proofs are meant as tutorial material for the qualifiers and to prepare for more advanced discussions of iterative methods that you may encounter in other classes such as Numerical Linear Algebra, Numerical PDE's via various methods, numerical optimization (deterministic and stochastic) etc. You are encouraged to consult the literature for other comments and alternate proofs of the results. The texts cited in Set 10 are useful for this with Saad's and Hackbusch's books of particular interest.

### Graded Homework 2 (pdf). Note that the program is Gauss transformation based and factorization only. It includes rectangular matrices. The next programming assignment will use this code and add Householder reflectors to study the stability and accuracy of solving linear systems and least squares problems by LU factorization and orthogonal transformations..

### Study Questions Homework 3 (pdf) is a set of problems related to least squares and transformation complexity.

### Study Questions Homework 2 (pdf) is a set of problems on triangular matrices and LU factorization.

### Graded Homework Solution Submission: Expected results comprise

- A PDF document with your solutions to any written problems in the assignment. This file should be kept separate from the files containing the solution for the programming problem.
- A PDF document describing your solutions as prescribed in the notes on writing up a programming solution posted on the class website.
- The source code, makefiles, and instructions on how to compile and execute your code including the Math Department machine used, if applicable. You may be asked to demonstrate your code on problems chosen by Tejas. You will use these routines and files to do so.
- Code documentation should be included in each routine.
- All text files that do not contain code or makefiles must be PDF files.
**Do not send Microsoft word files of any type or any other text processing input/wysiwyg files.**

The files should be placed in a zip file or other standard compressed format (please check with Tejas if you plan to use a compression other than zip.). You should organize the files in directories: one for the written solutions and any supporting figures or documents; one for the programming solution document and any supporting figures if not included in the PDF; one for code and supporting files;**Do not submit large amounts of essentially raw data. Part of the assignment is to effectively write a document so the reader does not have to analyze your data to assess your claims.**

The zip file should have the file name: LASTNAME_FIRSTNAME_gradedhw1.zip for the first one and with the number updated for subsequent assignments. These results should be submitted by 11:59 PM on the due date using the Canvas system.### Graded Homework 1 (pdf).

### Study Questions Homework 1 (pdf) is a set of problems on representation and numerics.