Does anyone have notes or paper on the calculation of eigenvalues/vectors for Toeplitz matrices?ThxChristian

QuoteOriginally posted by: christianbianDoes anyone have notes or paper on the calculation of eigenvalues/vectors for Toeplitz matrices?ThxChristianHere's an article by Gene Golub (of Golub/Van Loan book) for tridiagonal matricesToeplitzThis is what I use in some cases.As far as I know I think one can only find bounds for general case.General

Thx, I was exactly looking for something like Gene Golub paper (tridiagonal, symmetric and Toeplitz) Thx a lotCiao

QuoteOriginally posted by: christianbianThx, I was exactly looking for something like Gene Golub paper (tridiagonal, symmetric and Toeplitz) Thx a lotCiaoYou're welcome. Just out of curiosity, what are you using it for? Finite difference?

yes, I want to understand why Explicit euler is unstable for certain values of of k/(h^2)I like to have the 'full picture'........

QuoteOriginally posted by: christianbianyes, I want to understand why Explicit euler is unstable for certain values of of k/(h^2)I like to have the 'full picture'........Clear. With Toeplitz matrices you can also show that the Crank Nicolson scheme for BS produces complex eigenvalues and thus wiggly-wobbly oscillations at the strike price, especiallly for delta.BTW the matrix is not symmetric in this case.

Cuchulainn beat me into answering this question. It is interesting to know that there are systems which are modelled by non-symmetric toeplitz matrices. I always come across symmetric systems, but then I am an electrical engineer and not a quant . QuoteOriginally posted by: CuchulainnBTW the matrix is not symmetric in this case.

and Cr-Ni will be my next chap.......so I already have a good insight.....

QuoteOriginally posted by: greenmaxCuchulainn beat me into answering this question. I'll try to restrain myself next time

QuoteOriginally posted by: christianbianand Cr-Ni will be my next chap.......so I already have a good insight.....If you are doing FDM then a subclass of Toeplitz matrices are those whose diagonal elements A(i,i) > and off-diagonal elements are negative. These are important for the MONOTONIC FDM schemes and the matrices are called M matrices (their inverse has positive values).For example, exponentially fitted schemes are montone, but not Crank Nicolson, for example.Monotonic schemes are discussed in the Soviet literature of the time. They preserve PDE invariance. FDM

Hi Cuch,I was try to understand the Gollub papers but I got stuck in the middle of the first page when founding the lambda. below the passages= A[sin(j − 1)T + sin(j + 1)T] + B[cos(j − 1)T + cos(j + 1)T]That becomes (this is mine...)= A[sin (jT) + sin (-T) + sin (jT) + sin (T)] + B[cos (jT) + cos (-T) + cos ( jT) + cos (T)]butsin(-T) + sin (T) =0cos(-T) + cos (T) =2 cos (T)So how can he get ?= A(2 sin jT cos T) + B(2 cos T cos jT)My problem is the cos(T) after 2 sin (jT)ThxChristian

Hi ChristianYou need the following formulae I think:sin(a + b) = sina.cosb +cosa.sinbsin(a - b) = sina.cosb -cosa.sinbcos(a + b) = cosa.cosb -sina.sinbcos(a - b) = cos.cosb +sina.sinbregardsDD P.S. I kind of forgot these formulae, I had to dig into the grey cells before I could recall them

ok, now it's official, I owe you drinks......so let me know when you are going to be in London!and thanks

QuoteOriginally posted by: christianbianok, now it's official, I owe you drinks......so let me know when you are going to be in London!and thanksA pint of Guinness then

my irish friends told me that there are better stout.....just lookinf forward to it.parli anche italiano, giusto?io ho vissuto a delft per sei mesi come ricercatore econometrico con qualche viaggio a Amsterdam per i fine settimana. Bella citta'