Sentence examples for matrix with bandwidth from inspiring English sources

where is a symmetric, banded matrix with bandwidth, given by (2.3).

More precisely, given (SL) and the (imposed and natural) boundary conditions, then we show that this eigenvalue problem is equivalent with an algebraic eigenvalue problem for a real-symmetric, banded matrix with bandwidth, and we will construct this matrix explicity.

The paper [4] presents superfast (i.e., with numerical operations) and stable algorithms for the computation of some of the eigenvalues for a real-symmetric and banded matrix with bandwidth, where or for the most interesting division-free algorithms.

Then the construction of Section 5 transforms the Sturm-Liouville eigenvalue problem (given by (4.1) and (4.2)) of Section 4 into an equivalent algebraic eigenvalue problem for a real-symmetric, banded matrix with bandwidth.

The discretization of a second order Sturm-Liouville equation (1.1). of higher order leads to a banded matrix with bandwidth with, and then even Dirichlet boundary conditions lead for the discrete problem to the boundary conditions, which have to be complemented by additional "natural boundary conditions" in the usual way.

deriving the transform to an explicit algebraic algebraic eigenvalue problem for a symmetric, banded matrix with bandwidth, providing the required formulas, so that an implementation of the construction is easily "accessible" for the reader, proving that the construction is always successful under the conditions (4.4) and (4.7) (which is the contents of Theorem 6.1).

As is shown in [1] and used in [4] the algebraic eigenvalue problems for real-symmetric, banded matrices with bandwidth are equivalent to eigenvalue problems for self-adjoint Sturm-Liouville difference equations of order with Dirichlet boundary conditions.

The equivalence via Lemma 2.3 and Proposition 3.2 directly leads in general to a banded symmetric matrix with larger bandwidth.

The parallel block inverse matrix algorithm for the approximated CFR banded matrix with the bandwidth of Q 1 requires the complexity O[3N(Q 1+1)2].

Cluster crossing is the sum along the antidiagonal direction in the connectivity matrix with a bandwidth ( tilde{m} ) and takes a minimum at the cluster boundaries between clusters, i.e., each cluster forms a "peak" in the cluster-crossing curve [23].

In the figures, the BER performances of conventional low-complexity MMSE-FDE method for CP-OFDM of using the approximated banded matrix with the bandwidth of Q 1=2 and Q 1=15 [10], and the OLA-MMSE-FDE and FAST-MMSE-FDE methods for TS-OFDM with the Maclaurin's expansion order of Q 2=1 [14] are also shown as the purpose of comparisons with the proposed TDE method.