Isn't he this guy ? (kidding, there is no h, you are right).BTW there be no 'h' in Nicolson..

Isn't he this guy ? (kidding, there is no h, you are right).BTW there be no 'h' in Nicolson..

- Cuchulainn
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You are not alone! Numerical analysts know these things,

Ooops... I used CN schemes for years believing that Nicolson was a man ! These schemes are one of the most used schemes in numerical analysis, and I am just noticing right now that it is also a great contribution to gender equality. Thanks for the precision and the history reminder.You are not alone! Numerical analysts know these things,

- Cuchulainn
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You're welcome. BTW I see that Jim Douglas Jr. passed few years ago.

https://sinews.siam.org/Details-Page/Ob ... Douglas-Jr

Peter Lax is still here.

https://sinews.siam.org/Details-Page/Ob ... Douglas-Jr

Peter Lax is still here.

Jim Douglas is the one to be credited for ADI methods ? I did not know that either. Thanks again.You're welcome. BTW I see that Jim Douglas Jr. passed few years ago.

https://sinews.siam.org/Details-Page/Ob ... Douglas-Jr

Peter Lax is still here.

Concerning Lax, to me he is a little bit scary : Lax-Milgram, Lax-Wendroff, Lax Friedrichs...all those results are really famous one. My very humble contribution to his work (together with Monsieur Philippe !) is to propose a more general formula than the Hopf-Lax one to solve Jacobi-Bellman equations (the theoretical analysis behind this work is another paper to release :/).

Last edited by JohnLeM on April 8th, 2019, 12:44 pm, edited 1 time in total.

- FaridMoussaoui
**Posts:**507**Joined:****Location:**Genève, Genf, Ginevra, Geneva

You should also mention Olga Ladyzhenskaya

First proof of the convergence of FD schemes for the NS equations.

First proof of the convergence of FD schemes for the NS equations.

- Cuchulainn
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JD invented ADI with Rachford.Jim Douglas is the one to be credited for ADI methods ? I did not know that either. Thanks again.You're welcome. BTW I see that Jim Douglas Jr. passed few years ago.

https://sinews.siam.org/Details-Page/Ob ... Douglas-Jr

Peter Lax is still here.

Concerning Lax, to me he is a little bit scary : Lax-Milgram, Lax-Wendroff, Lax Friedrichs...all those results are really famous one. My very humble contribution to his work (together with Monsieur Philippe !) is to propose a more general formula than the Hopf-Lax one to solve Jacobi-Bellman equations (the theoretical analysis behind this work is another paper to release :/).

I once gave a talk on my PDE stuff at a conference. At the time the names of those attending the lectures were not known to me; Douglas, Lax, Wendroff, Strang, Kreiss, Dahlquist, Raviart, Janenko, Dahlquist, Cathleen Synge Morawetz.

Scary

- FaridMoussaoui
**Posts:**507**Joined:****Location:**Genève, Genf, Ginevra, Geneva

The 1955 paper about ADI was Peaceman & Rachford. Peaceman also co-authored a paper with Douglas about ADI.

- Cuchulainn
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? Didn't you quoted in your paper this book as having been written in 1964 ?ADE (1950s)

- FaridMoussaoui
**Posts:**507**Joined:****Location:**Genève, Genf, Ginevra, Geneva

The book in russian was published in 1960. The 1964 was a translation.

The Russian mathematicians publish a lot in russian. So there is some time to be aware of their work if you don't understand russian.

PS: When I said Russians, I meant Soviets ...

The Russian mathematicians publish a lot in russian. So there is some time to be aware of their work if you don't understand russian.

PS: When I said Russians, I meant Soviets ...

Last edited by FaridMoussaoui on April 8th, 2019, 6:39 pm, edited 1 time in total.

- Cuchulainn
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I studied Russian as undergraduate as preparation.. VK Saul'yev was Lithuanian.

I wrote the 1st article on ADE for option pricing., as I did with Alexander Levin on Soviet Spliting.

https://papers.ssrn.com/sol3/papers.cfm ... id=1552926

https://www.researchgate.net/publicatio ... _equations

https://core.ac.uk/download/pdf/39665447.pdf

etc.

I wrote the 1st article on ADE for option pricing., as I did with Alexander Levin on Soviet Spliting.

https://papers.ssrn.com/sol3/papers.cfm ... id=1552926

https://www.researchgate.net/publicatio ... _equations

https://core.ac.uk/download/pdf/39665447.pdf

etc.

- Cuchulainn
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"Soviet Splitting" (aka LOD) is better than ADI.

- Cuchulainn
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JohnLeM,

Looks like those kernels (and RKHS) that you mention have many applications.

Can we say that kernels allow us to define metrics and norms on probability measures? Then you can use the artillery of Functional Analysis bear, as I attempted to introduce before it was shot down. People like their comfort zones.

https://forum.wilmott.com/viewtopic.php?f=34&t=101293&p=826665&hilit=Cauchy#p826665

I see that it is even possible to use kernels instead of Kolmogorov-Smirnov. Are Cauchy sequences hiding in kernel methods?

**Beware: some folk think that Cauchy sequences caused the financial crisis.**

Looks like those kernels (and RKHS) that you mention have many applications.

Can we say that kernels allow us to define metrics and norms on probability measures? Then you can use the artillery of Functional Analysis bear, as I attempted to introduce before it was shot down. People like their comfort zones.

https://forum.wilmott.com/viewtopic.php?f=34&t=101293&p=826665&hilit=Cauchy#p826665

I see that it is even possible to use kernels instead of Kolmogorov-Smirnov. Are Cauchy sequences hiding in kernel methods?

Hello. I am not sure that kernel methods can be credited for defining metrics on probability spaces, as we can define such objects without introducing kernel methods : for instance Wasserstein distance, log entropy distance, etc...JohnLeM,

Looks like those kernels (and RKHS) that you mention have many applications.

Can we say that kernels allow us to define metrics and norms on probability measures? Then you can use the artillery of Functional Analysis bear, as I attempted to introduce before it was shot down. People like their comfort zones.

https://forum.wilmott.com/viewtopic.php?f=34&t=101293&p=826665&hilit=Cauchy#p826665

I see that it is even possible to use kernels instead of Kolmogorov-Smirnov. Are Cauchy sequences hiding in kernel methods?

Beware: some folk think that Cauchy sequences caused the financial crisis.

However, to any such metric, I think that we can associate one (or infinitely many) kernels, with which we can define a functional space (or infinitely many), and Cauchy sequences.

I am not a specialist of Kolmogorov Smirnov test . But a possible consequence is that we can try using another distributions than the Kolmogorov distribution one for this test : is that already known ? This would lead to infinitely many different tests than the one using the Jacobi theta function. What could be the purpose of such a construction ? I am not sure but we could adapt the Kolmogorov Smirnov test to a specific applications, exactly as we do for PDE or Machine learning, for instance to lower the number of testing samples. Could that be interesting for the stat community ?

EDIT : I just read new posts in this quite related thread, and found out that @Cuchullain posted a reference : https://arxiv.org/pdf/0805.2368.pdf that seems to give some good first answers to applications of kernels to Kolmogorov Smirnov-like test. I think that we could here contribute to this reference, giving more general and more precise testings, if there is any interest for such an approach.

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