Principles of Scientic Computing Nonlinear Equations and Optimization
David Bindel and Jonathan Goodman last revised March 6, 2006, printed March 6, 2009
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1
Introduction
This chapter discusses two re
Principles of Scientic Computing Monte Carlo methods
David Bindel and Jonathan Goodman last revised April 20, 2006, printed April 16, 2009
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Monte Carlo means using random numbers in scientic computin
Principles of Scientic Computing Linear Algebra II, Algorithms
David Bindel and Jonathan Goodman last revised March 2, 2006, printed February 26, 2009
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1
Introduction
This chapter discusses some of t
Bindel
Scientic Computing (G63.2043.001/G22.2112.001)
Homework 11
1. Using the technique described in Section 3.4, write a function g such
that for U Unif(0, 1), T = g (U ) has a Weibull distribution:
Bindel
Scientic Computing (G63.2043.001/G22.2112.001)
Homework 10 example
When you use the ODE solvers in MATLAB and then write scripts to automatically produce the plots, you use several pieces of so
Bindel
Scientic Computing (G63.2043.001/G22.2112.001)
Homework 10
Recall the equation for a pendulum is
(t) + sin(t) = 0.
This equation can be converted into standard rst-order form, and Octave
and M
Bindel
Scientic Computing (G63.2043.001/G22.2112.001)
Homework 9
1. (This problem is adapted from problem 3.4 of Ascher and Petzold).
The implicit midpoint rule satises
yn+1 = yn + hf
yn + yn+1
2
.
(a
Bindel
Scientic Computing (G63.2043.001/G22.2112.001)
Homework 8
1. Write a routine (in MATLAB or C+) to form the Newton divided differences and evaluate the interpolant and its derivatives. Your func
Bindel
Scientic Computing (G63.2043.001/G22.2112.001)
Homework 7
1. Write Newtons iteration formula for the equation f (x) = x2 a.
Show by a computational experiment that the formula is asymptotically
Bindel
Scientic Computing (G63.2043.001/G22.2112.001)
Homework 6
1. Download the code from the web page: cholesky.cc, cholesky.h,
test cholesky.cc, time cholesky.cc, Makefile, and readme.txt.
Read rea
Bindel
Scientic Computing (G63.2043.001/G22.2112.001)
Homework 5
1. The condition number for computing the action of a matrix A is
(A) =
=
=
A(x + x) Ax / Ax
(x + x) x / x
Ax / Ax
x / x
Ax / x
.
Ax /
Principles of Scientic Computing Dynamics and Dierential Equations
David Bindel and Jonathan Goodman last revised April 7, 2006, printed April 4, 2009
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Many dynamical systems are modeled by rst order
Principles of Scientic Computing Approximating functions
David Bindel and Jonathan Goodman last revised April 1, 2006, printed March 27, 2009
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Scientic computing often calls for representing or appro