# CPS Qualifying Exam Review Questions

###### Answered by CPS students, Spring 2010

#### CPS 5401

**Sample Questions**

**Fall 2009 and Fall 2010**

**(AZ)1)** **Basic Unix commands.**

**(GC)2)** **Create a simple Makefile.**

**3)** **Basic compiler options of g++ and gcc compiler (-I,-L,-l,-c,-o).**

**(GC) 4)** **Basic MPI commands**

**5)** **What is the difference between MPI and Open MP?**

**6)** **What is the difference between Distributed Memory Systems (Clusters), Shared Memory Systems, and General Distributed Computing?**

**7)** **What do you know about job scheduling (Torque, Sun Grid Engine, Windows HPC etc.).**

**8)** **What is distributed computing?**

**9)** **Development tools for C, C++, and FORTRAN**

**(CS) 10)** **Write a program for matrix multiplication in C++ or FORTRAN.**

**11)** **Debugging.**

**(CT)12)** **Parallel method for calculating an integral**

**(CT)13)** **Parallel Monte Carlo Method for calculating an integral.**

**(JP)14)** **Newton's method** *(PDF file)*

**(JP)15)** **Newton method with different starting points (parallel programming)** *(PDF file)*

**16)** **Row-major order versus column-major order in matrices.**

**17)** **Visualization (Matlab, Excel, GNU PLOT etc.)**

**(CF)18)** **Gauss elimination, LU decomposition** *(PDF file) * *Gauss elimination, LU decomposition**(Word file)*

**(CF)19)** **General information about iterative solvers (Jacobi, Gauss-Seidel)***(PDF file)* **General information about iterative solvers (Jacobi, Gauss-Seidel)***(Word file)*

**20)** **What do you know about numerical libraries for linear algebra( BLAS, LAPACK etc.) libraries?**

**(OL)22)** **Basics of FDM method (finite differences, numerical differentiation)**. *(PDF file)*

**(OL)23)** **Explicit FDM method .** *(PDF file)*

**(OL)***24) I***mplicit FDM method**

**25)** **Euler method and numerical integration of systems of ODE.**(????)

**27)** **Calculate mean value and variance by using parallel computing.**

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**28) Find the following stochastic integral.**

29) Solve the following stochastic differential equation by using Euler-Maruyama method.

(PA) 30) **Least Squares problem, Linear regression.** *(PDF file)*

*31) Inverse Problems*

**32)** **Describe the basic types of attractors (e.g. fixed point, limit cycle, limit tori, strange attractor).**

**33)** **Give short list of typical BVP (e.g. heat transfer equation, wave equation).**General Information About Iterative Solvers.pdf