# Incremental algorithm for matrix eigenvalues

I try to solve the following problem:
Given a stream of symmetric matrices $A_0, A_1, ...,A_n$ such that $A_i$ is different from $A_{i-1}$ only in one place, I want to compute the eigenvalues of $A_i$.
Since the matrices are very large, computing the eigenvalues from scratch isn't efficient (and since the matrices are different only in one place, that's also not very smart..), and I try to find how to calculate the eigenvalues of $A_i$ using the eigenvalues of $A_{i-1}$.

Any help will be welcomed,

Thanks

• Perhaps you could try finding a zero of the determinant using Newton's method - this presumes they are distinct, of course. Apr 23 '15 at 16:14
• So if the matrices are symmetric and change only in one place, that means you change only the diagonal?
– cfh
Apr 23 '15 at 16:32
• ieeexplore.ieee.org/document/1529967 Only computes the eigenvector corresponding to the dominant eigenvalue though. Jul 31 '18 at 14:20