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How to test a function for condition and stabilty?
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How can I test the condition and stability of the following function, for values $x=0$, $x=0.25$ and $x=10^-5$?
$$
f(x) = frac1-cos(2x)x
$$
What should one do here? For condition, I think I should do the following:
$$
K = left|fracf'(x)f(x) cdot xright|
$$
and check if it's $>> 1$ or $< 10$.
1) Am I right for the condition? And how to check for that $x$ values given above? If not, how would be the right way?
2) How to check the stability also for that values?
Thank you in advance!!
numerical-methods numerical-optimization stability-in-odes stability-theory condition-number
edited Jul 19 at 23:02
Somos
11.6k1933
asked Jul 19 at 21:14
ZelelB
1256
add a comment |Â
up vote
0
down vote
favorite
How can I test the condition and stability of the following function, for values $x=0$, $x=0.25$ and $x=10^-5$?
$$
f(x) = frac1-cos(2x)x
$$
What should one do here? For condition, I think I should do the following:
$$
K = left|fracf'(x)f(x) cdot xright|
$$
and check if it's $>> 1$ or $< 10$.
1) Am I right for the condition? And how to check for that $x$ values given above? If not, how would be the right way?
2) How to check the stability also for that values?
Thank you in advance!!
numerical-methods numerical-optimization stability-in-odes stability-theory condition-number
edited Jul 19 at 23:02
Somos
11.6k1933
asked Jul 19 at 21:14
ZelelB
1256
You could say $cos 2x = 1-2sin^2 x$ and then $f(x) = frac 2sin^2 xx$ and you might have some experience already with the function $frac sin xx$
– Doug M
Jul 19 at 21:34
because of the undefined form 0/0 you mean?
– ZelelB
Jul 19 at 21:44
Your function is undefined at $0.$ However, the limit exists.
– Doug M
Jul 19 at 21:45
yep, but how to answer the questions above? What should I do in the exam for this problem?
– ZelelB
Jul 19 at 21:45
would be greateful for any help! I have my last exam tomorrow, and this comes every time :/
– ZelelB
Jul 19 at 22:19
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
How can I test the condition and stability of the following function, for values $x=0$, $x=0.25$ and $x=10^-5$?
$$
f(x) = frac1-cos(2x)x
$$
What should one do here? For condition, I think I should do the following:
$$
K = left|fracf'(x)f(x) cdot xright|
$$
and check if it's $>> 1$ or $< 10$.
1) Am I right for the condition? And how to check for that $x$ values given above? If not, how would be the right way?
2) How to check the stability also for that values?
Thank you in advance!!
numerical-methods numerical-optimization stability-in-odes stability-theory condition-number
edited Jul 19 at 23:02
Somos
11.6k1933
asked Jul 19 at 21:14
ZelelB
1256
How can I test the condition and stability of the following function, for values $x=0$, $x=0.25$ and $x=10^-5$?
$$
f(x) = frac1-cos(2x)x
$$
What should one do here? For condition, I think I should do the following:
$$
K = left|fracf'(x)f(x) cdot xright|
$$
and check if it's $>> 1$ or $< 10$.
1) Am I right for the condition? And how to check for that $x$ values given above? If not, how would be the right way?
2) How to check the stability also for that values?
Thank you in advance!!
numerical-methods numerical-optimization stability-in-odes stability-theory condition-number
edited Jul 19 at 23:02
Somos
11.6k1933
asked Jul 19 at 21:14
ZelelB
1256
edited Jul 19 at 23:02
Somos
11.6k1933
edited Jul 19 at 23:02
Somos
11.6k1933
edited Jul 19 at 23:02
Somos
11.6k1933
11.6k1933
asked Jul 19 at 21:14
ZelelB
1256
asked Jul 19 at 21:14
ZelelB
1256
asked Jul 19 at 21:14
ZelelB
1256
1256
You could say $cos 2x = 1-2sin^2 x$ and then $f(x) = frac 2sin^2 xx$ and you might have some experience already with the function $frac sin xx$
– Doug M
Jul 19 at 21:34
because of the undefined form 0/0 you mean?
– ZelelB
Jul 19 at 21:44
Your function is undefined at $0.$ However, the limit exists.
– Doug M
Jul 19 at 21:45
yep, but how to answer the questions above? What should I do in the exam for this problem?
– ZelelB
Jul 19 at 21:45
would be greateful for any help! I have my last exam tomorrow, and this comes every time :/
– ZelelB
Jul 19 at 22:19
add a comment |Â
You could say $cos 2x = 1-2sin^2 x$ and then $f(x) = frac 2sin^2 xx$ and you might have some experience already with the function $frac sin xx$
– Doug M
Jul 19 at 21:34
because of the undefined form 0/0 you mean?
– ZelelB
Jul 19 at 21:44
Your function is undefined at $0.$ However, the limit exists.
– Doug M
Jul 19 at 21:45
yep, but how to answer the questions above? What should I do in the exam for this problem?
– ZelelB
Jul 19 at 21:45
would be greateful for any help! I have my last exam tomorrow, and this comes every time :/
– ZelelB
Jul 19 at 22:19
You could say $cos 2x = 1-2sin^2 x$ and then $f(x) = frac 2sin^2 xx$ and you might have some experience already with the function $frac sin xx$
– Doug M
Jul 19 at 21:34
You could say $cos 2x = 1-2sin^2 x$ and then $f(x) = frac 2sin^2 xx$ and you might have some experience already with the function $frac sin xx$
– Doug M
Jul 19 at 21:34
because of the undefined form 0/0 you mean?
– ZelelB
Jul 19 at 21:44
because of the undefined form 0/0 you mean?
– ZelelB
Jul 19 at 21:44
Your function is undefined at $0.$ However, the limit exists.
– Doug M
Jul 19 at 21:45
Your function is undefined at $0.$ However, the limit exists.
– Doug M
Jul 19 at 21:45
yep, but how to answer the questions above? What should I do in the exam for this problem?
– ZelelB
Jul 19 at 21:45
yep, but how to answer the questions above? What should I do in the exam for this problem?
– ZelelB
Jul 19 at 21:45
would be greateful for any help! I have my last exam tomorrow, and this comes every time :/
– ZelelB
Jul 19 at 22:19
would be greateful for any help! I have my last exam tomorrow, and this comes every time :/
– ZelelB
Jul 19 at 22:19
add a comment |Â
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You could say $cos 2x = 1-2sin^2 x$ and then $f(x) = frac 2sin^2 xx$ and you might have some experience already with the function $frac sin xx$
– Doug M
Jul 19 at 21:34
because of the undefined form 0/0 you mean?
– ZelelB
Jul 19 at 21:44
Your function is undefined at $0.$ However, the limit exists.
– Doug M
Jul 19 at 21:45
yep, but how to answer the questions above? What should I do in the exam for this problem?
– ZelelB
Jul 19 at 21:45
would be greateful for any help! I have my last exam tomorrow, and this comes every time :/
– ZelelB
Jul 19 at 22:19