Inverting a band matrix - Computer Science Stack Exchange
Dec 3, 2015 · Firstly, unfortunately, the inverse of a band-limited matrix is a full (non-band-limited) matrix in ...
What is the bandwidth of a matrix? - Mathematics Stack Exchange
Mar 14, 2017 · Bandwidth of a matrix A is defined as the smallest non-negative integer K such that A(i, j) = 0 for |i - j| > K. Now, I am confused as the condition says that a[i,j] should be 0 and |i-j| of the same should be > K. I am not able to figure out why a[i,j] should be 0. Please help me clearing what K is and what does this condition evaluate to.
matrices - Band matrix $A$ with bandwidth $m$. Count number of ...
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How to compute the determinant of a tridiagonal Toeplitz matrix?
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Eigenvalues of a band matrix populated by all ones
Recall that the band matrix is a matrix that is zero everywhere except on the band around the main diagonal. Question: Can we find an expression for the eigenvalue of this matrix? linear-algebra
algorithms - Finding the bandwidth of a band matrix - Computer …
$\begingroup$ If the main problem is too many 0's in the matrix, a sparse matrix representation would help to iterate over only the non-zero elements. However, if the steps you describe are already too costly, creating this representation from a normal matrix representation would likely be too costly as well.
Explicit calculation of eigenvalues of banded Toeplitz matrix
Jun 5, 2015 · I found in Bottcher and Grudsky's "Spectral Properties of Toeplitz Matrices" a reference to the paper by W.F. Trench.
matrices - How do I build this band matrix in MATLAB?
of course you can just replace the vectors by "scalar_value * ones(1,N-k)", where k is by how much off the main diagonal we are and N is the dimension of the matrix. For example diag(-lambda_1*ones(1,N-1),1)
linear algebra - Determinant of tridiagonal (banded) matrix ...
Nov 15, 2017 · Struggling with homework. I know that this is a banded matrix ( bandwidth = 3) but I don't know how to approach computing the determinant. I tried to compute it with matlab for n= 3,..,7 but I didn't
linear algebra - Matrix-vector product of a banded matrix
Feb 3, 2016 · Also, a banded matrix can be likened in complexity to a rectangular matrix whole row dimension is equal to the bandwidth of the bank matrix. Thus, the work involved in performing operations such as multiplication falls significantly, often leading to huge savings in terms of calculation time and complexity.