Scientific Computing: Special Topic in Computer Science

CSE 5400/4510
Florida Institute of Technology
Instructor: Debasis Mitra

Department: Computer Sciences


Science and engineering practices significantly depend on computation. In a spiral fashion, the availability of faster computers fuels data explosion in all branches of science, and in turn demands better computing resources. Developing efficient algorithms is a part of this equation. Hence, this course! Most of the algorithms in this area are primarily numerical (i.e., on the domain of real numbers or floating-point numbers). We go beyond the theoretical understanding of numerical analysis in this course, and code some of the basic and semi-advanced algorithms, to understand their structures and resource usage patterns. From this course, the students are expected to become "wiser" in coding mathematical operations that are bread and butter for most scientists, engineers, and even, financial and medical professionals these days. STUDENTS WITH CODING SKILL FROM ANY SCIENCE, ENGINEERING AND MATH DISCIPLINES ARE WELCOME.

The syllabus

Catalog Description: None at the moment! This is a Special Topic course for now.
Utilizing hands-on approach in coding scientific and mathematical algorithms, this course develops students' programming skills. Sample topics are linear algebra, inter- and extra-polation, data modeling, classification, inverse theory, etc.

Text book is "Numerical Recipes 3rd Edition: The Art of Scientific Computing," by William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery, Cambridge University Press, ISBN 0-521-75033-4.
Site at amazon, and
its site , also here.


A linear algebra basics book page
A Cornell SciComp Class page
C++ Linear Algebra codes:
Some math encyclopedia-type resources:

A free text-book from Mathworks .
A copy-rtd easy tutorial for sqr matrix-svd algorithm.
painless-conjugate-gradient, from Stanford
RidderMethod paper

TopoSurface Rep-KovalevskyOrig1999.pdf
Khalimski grid ref
A C++ resource: from IBM?

A resource on presentation styles.

+++++++++ Fall 2021 +++++++++++++++++

Olin Eng. 501OEC 137, TR 1400-1515, for the time being, we may change these. Zoom URL: to-be-decided

Plan/activities for the semester - is being continuously updated!

G-J elimination
L-U decomposition, Xinjie
ChrisTinkler-Cholesky _ QR Decomp decomposition, Chris
SVD, Conor Welch
CubicSpline-PolyInterp, Daniel Wall
BaryCentric Interpolation, Benjamin
Conjugate Gradient, Daniel Wall
Interpolation with scattered data , by Xinjie
Secant, False Positive, Ridders, and Brent methods' Presentation, Benjamin
Ch9.4: Newton-Raphson Method, Chris
Root Finding, Daniel Wall
============ Past Works ==============
Complexity theory-lite (7% with surgeon general's warning, etc.)

Tri- and Band-diagonal sparse matrices, Grayson
SVD decomposition, Mahbuba
Linear and Polynomial Interpolation, Grayson
Cubic Spline Interpolation, Rubens
Rational Interpolation, Rubens
Barycentric Interpolation and Coefficients, Mahbuba
Optimization_Brent's_Method, Mahbuba
========= Fall 2019 =================

Crawford 402 SCiComp TR 1400-1515
Plan/activities for the semester - is being continuously updated!

GaussJordan_20180822 by Valerie-Stephen
LU_Decomp by Lucas-Jerry
SVD decomposition by Joy Moore
Kriging Interpolation by Valerie-Stephen
Laplace Interpolation by Joy Moore
Tri_BandDiagonal by Valerie-Stephen
RBFInterpolation by Valerie-Stephen
QRDecomposition_20190910 by Valerie-Stephen
Cholesky by Valerie-Stephen
ConjugateGradient by Valerie-Stephen
My talk in Bio-department, 3:30pm, Oct-24-R, Life Sc. Bldg 130
JoyDatamodel15.0-15.2 by Joy Moore

======= Spring 2017 =======

CRF 401, TR 6:30-7:45pm, CSE 5400/4510

Plan/activities for the semester - is being continuously updated!

======= Spring 2014 =======

Class: Crawford 403 Mondays-Wednesdays 8-9:15pm.

Plan/activities for the semester - is being continuously updated!

Dr. Allen's lectures on numerical precision and Gauss-Jordan basics.
======= Spring 2013 ================
Class: Crawford 403 Wednesdays 8-10pm.

Plan/activities for the semester - is being continuously updated!

Syllabus for Spr13:
Ch 2 Linear Alg., Ch 3 Interpolation, Ch 6 Spl. Functions, Ch 9 Roots of Equation, Ch 10 Optimzation, Ch 13 Spectral Analysis, and Ch 10 Inverse theory (7 chapters, ~15 weeks)

Before preparing the lecture/demo you may like to look at my notes

Kim's Gauss-Jorddan elimination Ch2 talk
Jessie's LU decomposition Ch 2 talk
Shi and Bo's SVD and Conjugate Gradient Ch 2 talks
Yunfei and Hui's Plynomial Interpolation Ch 3 and, Multi-dimensional Interpolation Ch 3.6 presentations
Mike and Christian's Rational & Barycentric Interpolation Ch 3 talk
Kim & Jessie's Radial-basis Function interpolation Ch3 talk
Kim, Jessie & Christian's Newton-Raphson Ch9 1D root finding, talk
Mike and Vallerie Optimization Ch 10 talk
Yunfei and Hui's Optimization on 1D Ch10.3-4 presentation
Shi and Bo on nD Powell Ch10.7
Mike and Vallerie Convolution using FFT Ch 13.?, Convolution using FFT Ch 13.?, Wavelet basics Ch 13.?, Wavelet transform Ch 13.?, and more on use of Wavelet transform Ch 13.10.6-8 presentations.
Shi and Bo's slides on Linear eq solving with Wavelet Ch13.10.7

Spring 2012:

Class: Crawford 403 Wednesdays 8-10pm.

Plan/activities for the semester - is being continuously updated!

Raw numerical-simulation 3D image data:
(original: my Projects\Lbnl\MotnCorrc\RossPhantomData directory) download
Width=128, Height=128, Depth ("Number of Images")=90, but you can give any larger number on ImageJ
Image type=32-bit Real, Little Endian Byte order(Intel format)
Both groups: start with down sampled image, 128x128x90 is too large now!
'/' command gives orthogonal view, ImageJ also has 3D viewer plugin. Enjoy!
Spring 2011:

Class: Crawford 403 Wednesdays 8-10pm.

UG CSE4510-E11 students: please come to the above class, and let me know that you are UG student.

The course have mostly student presentations and discussion, along with coding & projects. We go over some chapters from the text for basic knowledge on the mathematical computing area, and then expect to code them. We do explore some tools in the area.

Plan/activities for the semester - is being continuously updated!

LUP module
Grid N, Scattered Data, Laplace
Linear Programming
Modeling Data Intro
Ch15- Data Modeling
Ch16- Expectation Maximization

Digital enlargement preserving information, by Nawar Kabbani and Gregory Beckham: Report
Detection of traffic signals from a moving car, by Daniel Eiland and Mahmoud Abdallah: Presentation, Report
Edge detection by MCMC algorithm with Gibbs Sampling, by Michael Sedvy: Report


Materials are copyrighted to me (year 2010). E-mail: dmitra at fit dt edu