MATLAB: How to create symmetric matrix that is stable

matrix

How to create symmetric matrix that is stable, i.e. Re(eigenvalue)<0?

Best Answer

Let D be the vector of desired eigenvalues. Then one such matrix is

compan(poly(D))

Credit: Tim Davis in https://www.mathworks.com/matlabcentral/newsreader/view_thread/252328

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MATLAB: How to keep ANN training result stable

The variations tend to come from

 1. The random number seed (I like rng(4151941))
 2. The random division of data
 3. The random initial weights

I generally use defaults except for a range of hidden node sizes

h = Hmin:dH:Hmax

Then for each value of h, train Ntrials (usually 10) models.

Sometimes a perusal of the Ntrials x numel(h) matrix of results causes me to change some parameter(s) and repeat.

I have posted zillions of examples in both the NEWSGROUP and ANSWERS. My tutorials are in the NEWSGROUP.

I always start using all defaults to get the lay of the land.

Reasonable searchwords to include are subsets of

 neural greg Hmin:dH:Hmax Ntrials

Post selected code with comments and/or error messages if you have further problems.

Hope this helps.

Thank you for formally accepting my answer

Greg

MATLAB: How to create positive semidefinite matrix from random value

https://www.mathworks.com/matlabcentral/answers/84287-positive-semi-definite-matrix-problem

A = rand(50);
A = 0.5 *(A+A');
issymmetric(A)
ans = logical
   1
d = eig(A)
d = 50×1
   -2.6403
   -2.3499
   -2.3084
   -2.1472
   -2.0568
   -1.9520
   -1.8574
   -1.5880
   -1.5540
   -1.4120
all(imag(d) == 0 & d >= 0)
ans = logical
   0
APos = A'*A;
issymmetric(APos)
ans = logical
   1
d = eig(APos)
d = 50×1
    0.0000
    0.0048
    0.0360
    0.0436
    0.0506
    0.0978
    0.1031
    0.1715
    0.1725
    0.1929
●
all(imag(d) == 0 & d >= 0)
ans = logical
   1

Best Answer

Related Solutions

MATLAB: How to keep ANN training result stable

MATLAB: How to create positive semidefinite matrix from random value

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