Thresholding to minimize round-off errors (hubbard) The 2019 Stack Overflow Developer Survey Results Are InLaw of Cosines for very acute angles, round-off errorHow to round off timestamp in milliseconds to nearest seconds?How to compute Fourier coefficients using a cubic spline-corrected FFT?Prof claimed that $arcsin x + arccos x$ does not always round to 90º under the same number of significant figures.Round-off: cross- vs. dot-productsNumerical analysis 1 round off errorsWhy is 'catastrophic cancellation' called so?Round Off Error AnalysisComputing Absolute and Relative Error Using Double PrecisionRound off to decimals
Identify This Plant (Flower)
"as much details as you can remember"
Aging parents with no investments
Should I use my personal e-mail address, or my workplace one, when registering to external websites for work purposes?
Can one be advised by a professor who is very far away?
Is bread bad for ducks?
Why not us interferometry to take a picture of Pluto?
Origin of "cooter" meaning "vagina"
What did it mean to "align" a radio?
What is the accessibility of a package's `Private` context variables?
Why hard-Brexiteers don't insist on a hard border to prevent illegal immigration after Brexit?
Time travel alters history but people keep saying nothing's changed
Have you ever entered Singapore using a different passport or name?
Geography at the pixel level
How come people say “Would of”?
Why do UK politicians seemingly ignore opinion polls on Brexit?
Loose spokes after only a few rides
Why was M87 targetted for the Event Horizon Telescope instead of Sagittarius A*?
What is the meaning of Triage in Cybersec world?
Multiply Two Integer Polynomials
Button changing it's text & action. Good or terrible?
Is there a symbol for a right arrow with a square in the middle?
How can I autofill dates in Excel excluding Sunday?
Can you compress metal and what would be the consequences?
Thresholding to minimize round-off errors (hubbard)
The 2019 Stack Overflow Developer Survey Results Are InLaw of Cosines for very acute angles, round-off errorHow to round off timestamp in milliseconds to nearest seconds?How to compute Fourier coefficients using a cubic spline-corrected FFT?Prof claimed that $arcsin x + arccos x$ does not always round to 90º under the same number of significant figures.Round-off: cross- vs. dot-productsNumerical analysis 1 round off errorsWhy is 'catastrophic cancellation' called so?Round Off Error AnalysisComputing Absolute and Relative Error Using Double PrecisionRound off to decimals
$begingroup$
I'm working through Hubbard's Vector Calculus text, and I'm a little fuzzy concerning a detail of one example:
He later asks you to analyze where the errors occur in formula 2.1.12, and I see that
$$
1-2cdot10^10=1-20000000000=-19999999999=-20000000000=-2cdot10^10
$$
due to computing to 10 significant digits--the "error" is that the 1 essentially disappears in the subtraction.
My question is how the 1 becomes $-10^10$ from the second matrix to the third. It would seem that, out to 10 significant figures, we would have
$$
1-10^10=1-10000000000=-9999999999neq-10^10.
$$
Where am I going wrong?
algebra-precalculus numerical-methods rounding-error
asked Mar 23 at 15:57
interrogativeinterrogative
265111
$endgroup$
add a comment |
$begingroup$
I'm working through Hubbard's Vector Calculus text, and I'm a little fuzzy concerning a detail of one example:
He later asks you to analyze where the errors occur in formula 2.1.12, and I see that
$$
1-2cdot10^10=1-20000000000=-19999999999=-20000000000=-2cdot10^10
$$
due to computing to 10 significant digits--the "error" is that the 1 essentially disappears in the subtraction.
My question is how the 1 becomes $-10^10$ from the second matrix to the third. It would seem that, out to 10 significant figures, we would have
$$
1-10^10=1-10000000000=-9999999999neq-10^10.
$$
Where am I going wrong?
algebra-precalculus numerical-methods rounding-error
asked Mar 23 at 15:57
interrogativeinterrogative
265111
$endgroup$
$begingroup$
yeah, Technically, that should be $-9999999999$. But does that one change suddenly rescue the calculation and give you the correct result? Or does it just change the amount of error?
$endgroup$
– Paul Sinclair
Mar 24 at 2:35
add a comment |
$begingroup$
I'm working through Hubbard's Vector Calculus text, and I'm a little fuzzy concerning a detail of one example:
He later asks you to analyze where the errors occur in formula 2.1.12, and I see that
$$
1-2cdot10^10=1-20000000000=-19999999999=-20000000000=-2cdot10^10
$$
due to computing to 10 significant digits--the "error" is that the 1 essentially disappears in the subtraction.
My question is how the 1 becomes $-10^10$ from the second matrix to the third. It would seem that, out to 10 significant figures, we would have
$$
1-10^10=1-10000000000=-9999999999neq-10^10.
$$
Where am I going wrong?
algebra-precalculus numerical-methods rounding-error
asked Mar 23 at 15:57
interrogativeinterrogative
265111
$endgroup$
I'm working through Hubbard's Vector Calculus text, and I'm a little fuzzy concerning a detail of one example:
He later asks you to analyze where the errors occur in formula 2.1.12, and I see that
$$
1-2cdot10^10=1-20000000000=-19999999999=-20000000000=-2cdot10^10
$$
due to computing to 10 significant digits--the "error" is that the 1 essentially disappears in the subtraction.
My question is how the 1 becomes $-10^10$ from the second matrix to the third. It would seem that, out to 10 significant figures, we would have
$$
1-10^10=1-10000000000=-9999999999neq-10^10.
$$
Where am I going wrong?
algebra-precalculus numerical-methods rounding-error
algebra-precalculus numerical-methods rounding-error
asked Mar 23 at 15:57
interrogativeinterrogative
265111
asked Mar 23 at 15:57
interrogativeinterrogative
265111
edited Mar 23 at 16:34
interrogative
asked Mar 23 at 15:57
interrogativeinterrogative
265111
asked Mar 23 at 15:57
interrogativeinterrogative
265111
asked Mar 23 at 15:57
interrogativeinterrogative
265111
265111
$begingroup$
yeah, Technically, that should be $-9999999999$. But does that one change suddenly rescue the calculation and give you the correct result? Or does it just change the amount of error?
$endgroup$
– Paul Sinclair
Mar 24 at 2:35
add a comment |
$begingroup$
yeah, Technically, that should be $-9999999999$. But does that one change suddenly rescue the calculation and give you the correct result? Or does it just change the amount of error?
$endgroup$
– Paul Sinclair
Mar 24 at 2:35
$begingroup$
yeah, Technically, that should be $-9999999999$. But does that one change suddenly rescue the calculation and give you the correct result? Or does it just change the amount of error?
$endgroup$
– Paul Sinclair
Mar 24 at 2:35
$begingroup$
yeah, Technically, that should be $-9999999999$. But does that one change suddenly rescue the calculation and give you the correct result? Or does it just change the amount of error?
$endgroup$
– Paul Sinclair
Mar 24 at 2:35
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3159475%2fthresholding-to-minimize-round-off-errors-hubbard%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3159475%2fthresholding-to-minimize-round-off-errors-hubbard%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
yeah, Technically, that should be $-9999999999$. But does that one change suddenly rescue the calculation and give you the correct result? Or does it just change the amount of error?
$endgroup$
– Paul Sinclair
Mar 24 at 2:35