Bindel, Spring 2012
Intro to Scientic Computing (CS 3220)
Week 14: Wednesday, May 2
Summary
Error analysis and oating point
You should know about relative vs absolute error, forward error, backward
er
Bindel, Fall 2012
Intro to Scientic Computing (CS 3220)
Week 6: Monday, Mar 5
Iterative and Direct Methods
So far, we have discussed direct methods for solving linear systems and least
squares problem
Bindel, Fall 2012
Intro to Scientic Computing (CS 3220)
Week 5: Wednesday, Feb 29
Of cabbages and kings
The past three weeks have covered quite a bit of ground. Weve looked at
linear systems and least
Bindel, Fall 2012
Intro to Scientic Computing (CS 3220)
Week 5: Monday, Feb 27
Least squares reminder
Last week, we started to discuss least squares solutions to overdetermined
linear systems:
minimiz
Bindel, Fall 2012
Intro to Scientic Computing (CS 3220)
Week 5: Wednesday, Feb 22
Least squares: the big idea
Least squares problems are a special sort of minimization. Suppose A Rmn
and m > n. In gen
Bindel, Fall 2012
Intro to Scientic Computing (CS 3220)
Week 4: Wednesday, Feb 15
A summary
From Monday, you should have learned:
1. Gaussian elimination can be seen as the computation of a matrix fac
Bindel, Fall 2012
Intro to Scientic Computing (CS 3220)
Week 4: Monday, Feb 13
Gaussian elimination in matrix terms
To solve the linear system
4 4 2 x1
2
4 5 3 x2 = 3 ,
2 3 3 x3
5
by Gaussian elimin
Bindel, Fall 2012
Intro to Scientic Computing (CS 3220)
Week 3: Wednesday, Feb 8
Spaces and bases
I have two favorite vector spaces1 : Rn and the space Pd of polynomials of
degree at most d. For Rn ,
Bindel, Fall 2012
Intro to Scientic Computing (CS 3220)
Week 3: Monday, Feb 6
Subtle singularity
A square matrix A Rnn is called invertible or nonsingular if there is an
A1 such that AA1 = I . Otherwi
Bindel, Spring 2012
Intro to Scientic Computing (CS 3220)
Week 2: Wednesday, Feb 1
Use a routine, or roll your own?
The Matlab function fzero is a fast, reliable black-box root-nding algorithm based o
Bindel, Spring 2012
Intro to Scientic Computing (CS 3220)
Week 2: Monday, Jan 30
Overview
After this week (and the associated problems), you should come away with
some understanding of
Algorithms for
Bindel, Fall 2012
Intro to Scientic Computing (CS 3220)
Week 6: Wednesday, Mar 7
From Stationary Methods to Krylov Subspaces
Last time, we discussed stationary methods for the iterative solution of li
Bindel, Fall 2012
Intro to Scientic Computing (CS 3220)
Week 7: Monday, Mar 12
Newton and Company
Suppose f : Rn Rn is twice dierentiable. Then
f (x + x) = f (x) + f (x)x + O( x 2 ),
where f (x) denot
Bindel, Fall 2012
Intro to Scientic Computing (CS 3220)
Week 7: Wednesday, Mar 14
Line search revisited
In the last lecture, we briey discussed the idea of a line search to improve
the convergence of
Bindel, Spring 2012
Intro to Scientic Computing (CS 3220)
Week 14: Monday, Apr 30
Introduction
So far, our discussion of ODE solvers has been rather abstract. Weve talked
some about how to evaluate OD
Bindel, Spring 2012
Intro to Scientic Computing (CS 3220)
Week 13: Wednesday, Apr 25
The Runge-Kutta concept
Runge-Kutta methods evaluate f (t, y ) multiple times in order to get higher
order accuracy
Bindel, Spring 2012
Intro to Scientic Computing (CS 3220)
Week 13: Monday, Apr 23
Ordinary dierential equations
Consider ordinary dierential equations of the form
(1)
y = f (t, y )
together with the i
Bindel, Spring 2012
Intro to Scientic Computing (CS 3220)
Week 12: Wednesday, Apr 18
Adaptive error control
Last time, we discussed Simpsons rule for quadrature:
b
f (x) dx
I [f ] =
a
ba
(f (a) + 4f
Bindel, Spring 2012
Intro to Scientic Computing (CS 3220)
Week 12: Monday, Apr 16
Panel integration
Suppose we want to compute the integral
b
f (x) dx
a
In estimating a derivative, it makes sense to u
Bindel, Spring 2012
Intro to Scientic Computing (CS 3220)
Week 11: Wednesday, Apr 11
Truncation versus rounding
Last week, we discussed two dierent ways to derive the centered dierence
approximation t
Bindel, Spring 2012
Intro to Scientic Computing (CS 3220)
Week 11: Monday, Apr 9
Maximizing an interpolating quadratic
Suppose that a function f is evaluated on a reasonably ne, uniform mesh
cfw_xi n=
Bindel, Fall 2012
Intro to Scientic Computing (CS 3220)
Week 10: Monday, Apr 2
Hermite interpolation
For standard polynomial interpolation problems, we seek to satisfy conditions
of the form
p(xj ) =
Bindel, Fall 2012
Intro to Scientic Computing (CS 3220)
Week 9: Wednesday, Mar 28
Summary of last time
We spent most of the last lecture discussing three forms of polynomial interpolation. In each cas
Bindel, Fall 2012
Intro to Scientic Computing (CS 3220)
Week 9: Monday, Mar 26
Function approximation
A common task in scientic computing is to approximate a function. The
approximated function might
Bindel, Fall 2012
Intro to Scientic Computing (CS 3220)
Week 1: Wednesday, Jan 25
Binary oating point encodings
Binary oating point arithmetic is essentially scientic notation. Where in
decimal scient
Bindel, Fall 2012
Intro to Scientic Computing (CS 3220)
Week 1: Monday, Jan 23
Safe computing
If this class were about shooting rather than computing, wed probably start
by talking about where the saf
CS 3220 Spring 2010
Homework 1
Problem 1: Heath Computer Problem 1.3.
For (b), at a minimum, provide experimental results for double- and single-precision in
Matlab, plus one other device (perhaps a c
function [] = phi_test(W, s,h ) %PHI_TEST Summary of this function goes here % Detailed explanation goes here [i j] = find(W); n = randi(length(i); i = i(n); j = j(n); % i, j are indices of a weight t
function [phi, Ws, ss] = phi_sensitivity(W, s) %PHI_SENSITIVITY calculates the mean as well as the partials of phi % See http:/mathbin.net/89270 and http:/mathbin.net/89286 for full % derivation of th