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1·For a general banded matrix, discuss the sparsity pattern of the Q and R matrices from the QR decomposition of symmetric and non-symmetric tridiagonal matrices.

对于一般的带状矩阵，详述对对称与非对称三对角化矩阵做QR分解后，Q矩阵与R矩阵的稀疏元素分布型态。

2·Strang s analysis applies to so-called banded matrices. Most of the Numbers in a banded matrix are zeroes; the only exceptions fall along diagonal bands, at or near the central diagonal of the matrix.

Strang的分析被应用于所谓的带状矩阵上；带状矩阵的绝大多数项都是0；唯一的例外是矩阵中心或靠近矩阵中心的对角带。

3·The four kinds of method for symmetrization of the nonsymmetric and no. banded matrix equations of the mixed element and the associated approximate methods for analysis of some fluid-solid coupled d…

对于非对称、非带状混合元方程，提出了四种对称化方法及相应的分析耦合问题的近似方法。

4·In a signal-processing application, all the speed advantages offered by banded matrices would be lost if restoring the signal required multiplying it by a full matrix.

在信号处理应用程序中，如果恢复信号需要乘上一个“满”的矩阵，那么带状矩阵提供的所有的速度优势都将不复存在。

5·This matrix is symmetric and banded, the band being equal to four.

这个矩阵是对称的且是带状的，带宽等于四。

6·Floating point representation, Gaussian elimination with partial pivoting, scaling of computations with matrix size, banded and tri-diagonal systems, LU decomposition.

浮点数表示法，含部份换轴之高斯消去法，使用矩阵大小之计算尺度调整，带状及三角对角系统，LU分解。

7·Our study was found that two main reasons making the circular saw blades matrix distortion in quenching were banded structure and the unreasonable quenching process.

研究发现，原材料的带状组织和淬火工艺的不合理是造成锯片基体淬火变形的两个主要原因。

8·A banded sparse system matrix is obtained.

所得系统矩阵是一个带状稀疏矩阵。