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Random Slides for Numerical Analysis and Computing | MATH 541, Study notes of Mathematics

San Diego State University (SDSU)Mathematics

Prof. P. Blomgren

Material Type: Notes; Professor: Blomgren; Class: INTRO NUM ANALYS & COMPUT; Subject: Mathematics; University: San Diego State University; Term: Fall 2009;

Typology: Study notes

Pre 2010

Uploaded on 03/28/2010

koofers-user-5mq 🇺🇸

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Homework Comments

Numerical Analysis and Computing

Random Notes #51

2

Peter Blomgren,

h[email protected]i

Department of Mathematics and Statistics

Dynamical Systems Group

Computational Sciences Research Center

San Diego State University

San Diego, CA 92182-7720

http://terminus.sdsu.edu/

Fall 2009

Peter Blomgren, h[email protected]iRandom Notes #5 1

2— (1/11)

Homework Comments

Outline

1Homework Comments

Homework #2

Peter Blomgren, h[email protected]iRandom Notes #5 1

2— (2/11)

Homework Comments Homework #2

Somewhat Common Mistakes

1Please give some measure of speed — either

1Number of steps needed (robust), or

2execution time (may depend on what else is going on in the

background...).

2Don’t display failure message when the root is found.

Peter Blomgren, h[email protected]iRandom Notes #5 1

2— (3/11)

Homework Comments Homework #2

Function Calls

Cute idea: sending the mathematical function as a string argument

to the function —

file: bisection.m

function [ReturnValue] = bisection( fstring, a, b, TOL );

f = inline( fstring, ’x’ );

...

Matlab prompt

>> my root1 = bisection( ’sin(x)’, -0.2, 0.5, 1e-8 );

Peter Blomgren, h[email protected]iRandom Notes #5 1

2— (4/11)

Discover Study notes of Mathematics San Diego State University (SDSU)

Partial preview of the text

Download Random Slides for Numerical Analysis and Computing | MATH 541 and more Study notes Mathematics in PDF only on Docsity!

Homework Comments Numerical Analysis and Computing^ Random Notes

Peter Blomgren, 〈[email protected]

Department of Mathematics and Statistics^ Dynamical Systems GroupComputational Sciences Research Center^ San Diego State UniversitySan Diego, CA 92182-7720^ http://terminus.sdsu.edu/^ Fall 2009 Peter Blomgren, 〈[email protected]〉^

(^1) Random Notes #5 2

— (1/11)

Homework Comments

Outline^1 Homework Comments^ Homework #2^ Peter Blomgren,

〈[email protected]

(^1) 〉 Random Notes #5 2

— (2/11)

Homework Comments^

Homework #

Somewhat Common Mistakes^1 Please give

some^ measure of speed — either 1 Number of steps needed (robust), or 2 execution time (may depend on what else is going on in thebackground...). 2 Don’t display failure message when the root

is^ found.

Peter Blomgren,^ 〈[email protected]

(^1) 〉 Random Notes #5 2

— (3/11)

Homework Comments^

Homework #

Function Calls^ Cute idea: sending the mathematical function as a string argumentto the function —^ file:^ bisection.m^ function [ReturnValue] = bisection( fstring, a, b, TOL );f = inline( fstring, ’x’ );...^ Matlab prompt^ >> my^ root1 = bisection( ’sin(x)’, -0.2, 0.5, 1e-8 );^ Peter Blomgren,

〈[email protected]

(^1) 〉 Random Notes #5 2

— (4/11)

Homework Comments^

Homework #

Function Calls — Other Variants, 1^ file:^ bisection.m^ function [ReturnValue] = bisection( f, a, b, TOL );fa = f(a);fb = f(b);...^ Matlab prompt^ >> F = inline(’sin(x)’,’x’);>> G = inline(’sin(x) .* cos(x) .* exp(x)’,’x’);>> my^ root2 = bisection( F, -0.2, 0.5, 1e-8 );>> my^ root3 = bisection( G, -0.3, 0.4, 1e-10 );^ Peter Blomgren,

〈[email protected]

(^1) 〉 Random Notes #5 2

— (5/11)

Homework Comments^

Homework #

Function Calls — Other Variants, 2^ file:^ myGnarlyFunction.m^ function [ReturnValue] = myGnarlyFunction( x );ReturnValue =(exp(sin(x.cos(tan(x+pi/52))))+9).sin(cos(x));^ Matlab prompt^ >> r4 = bisection( @myGnarlyFunction, -0.2, 0.5, 1e-8 );^ Peter Blomgren,

〈[email protected]

(^1) 〉 Random Notes #5 2

— (6/11)

Homework Comments^

Homework #

Function Calls — help...^ For more information^ >> help function^ >> help punct^ See the entry for

@^ “At.”

>> help publish^ If you want to do fancy “publishing” of your code Peter Blomgren,^ 〈[email protected]

(^1) 〉 Random Notes #5 2

— (7/11)

Homework Comments^

Homework #

Publishing Example, 1/4^ file:^ test^ pub.m^ % % This is the main driver...% (cannot be a function for publishing)% xv = 1.4 :^

0.001 :^ 1.6;fxv = myGnarlyFunction(xv);r = bisection( @myGnarlyFunction, 1.4, 1.6, 1e-5 );% plot(xv,fxv);hold onaxis([min(xv) max(xv) min(fxv)1.05 max(fxv)1.05])plot(r,myGnarlyFunction(r),’ro’);grid ongrid minorhold off Peter Blomgren, 〈[email protected]

(^1) 〉 Random Notes #5 2

— (8/11)

Random Slides for Numerical Analysis and Computing | MATH 541, Study notes of Mathematics

Related documents

Partial preview of the text

Download Random Slides for Numerical Analysis and Computing | MATH 541 and more Study notes Mathematics in PDF only on Docsity!

Homework Comments Numerical Analysis and Computing^ Random Notes

Peter Blomgren, 〈[email protected]

Department of Mathematics and Statistics^ Dynamical Systems GroupComputational Sciences Research Center^ San Diego State UniversitySan Diego, CA 92182-7720^ http://terminus.sdsu.edu/^ Fall 2009 Peter Blomgren, 〈[email protected]〉^

Outline^1 Homework Comments^ Homework #2^ Peter Blomgren,

Somewhat Common Mistakes^1 Please give

some^ measure of speed — either 1 Number of steps needed (robust), or 2 execution time (may depend on what else is going on in thebackground...). 2 Don’t display failure message when the root

is^ found.

Function Calls — Other Variants, 2^ file:^ myGnarlyFunction.m^ function [ReturnValue] = myGnarlyFunction( x );ReturnValue =(exp(sin(x.cos(tan(x+pi/52))))+9).sin(cos(x));^ Matlab prompt^ >> r4 = bisection( @myGnarlyFunction, -0.2, 0.5, 1e-8 );^ Peter Blomgren,

Function Calls — help...^ For more information^ >> help function^ >> help punct^ See the entry for

@^ “At.”

>> help publish^ If you want to do fancy “publishing” of your code Peter Blomgren,^ 〈[email protected]

Publishing Example, 1/4^ file:^ test^ pub.m^ % % This is the main driver...% (cannot be a function for publishing)% xv = 1.4 :^

0.001 :^ 1.6;fxv = myGnarlyFunction(xv);r = bisection( @myGnarlyFunction, 1.4, 1.6, 1e-5 );% plot(xv,fxv);hold onaxis([min(xv) max(xv) min(fxv)1.05 max(fxv)1.05])plot(r,myGnarlyFunction(r),’ro’);grid ongrid minorhold off Peter Blomgren, 〈[email protected]