分别采用LSQR和ART算法对欠定方程组进行了层析成像计算。
LSQR and ART algorithms are applied separately to calculate tomography for the underdetermined system of equation.
这就是我们要解的方程组。
各种程序生成了不同的方程组——描述沙漠高原降雨量的作用，或触发哮喘的空气污染，或认知功能的多任务处理。
Programs produce sets of equations - describing the role of rainfall on a desert plateau, or air pollution in triggering asthma, or multitasking on cognitive function.
加州大学戴维斯分校环境科学与政策系教授黑斯廷斯，是世界上利用数学模型(方程组)来理解自然系统的顶级专家之一。
Hastings, a professor in the UC Davis Department of Environmental Science and Policy, is one of the world's top experts in using mathematical models (sets of equations) to understand natural systems.
在2002年，他就得出了一个能预测癌症演化和扩散方式的方程组，比如说染色体何时开始变得不稳定，使得癌细胞在转移中发生变异。
In 2002 he worked out equations that can predict the way cancer evolves and spreads, such as when mutations emerge in a metastasis and chromosomes become unstable.
用这个拉格朗日方法，你是不能保证解出这个方程组的,你只能对着它想。
There is no general method for solving the equations that you get from this method. You just have to think about them.
如果没有的话，我们继续往下，线性参数方程组。
OK, so if not, let's move on to linear parametric equations.
它所能做的就是解决这些方程组问题。
电与磁：麦克斯韦方程组。
Maxwell方程组是“非对称的”：电场有一个负电极子和一个正电极子，带着不同的电荷；但磁场却没有。
Maxwell's equations are "asymmetrical": electricity has an electron monopole and a proton monopole, each with opposite charge, but magnetism does not.
Meschach可以解稠密或稀疏线性方程组、计算特征值和特征向量和解最小平方问题，另外还有其它功能。
Meschach was designed to solve systems of dense or sparse linear equations, compute eigenvalues and eigenvectors, and solve least squares problems, among other things.
实际上，Maxwell方程组，描述了这两个场的旋度和散度。
Maxwell's equations actually tell you about div and curl of these fields.
，这是我的计划：线代的基本问题是用来解线性方程组（systemof linear equations）。
, this is my plan, the fundamental problem of linear algebra, which is to solve a system of linear equations.
我能够得到，我能够解决任意右侧部分b的这些方程组么？
Could I get, can I solve all these equations for every right hand side?
实际上，是讲Maxwell方程组。
And, in fact, something that is known as Maxwell's equations.
这种情况必然发生在,不可逆线性方程组的情况，且等号右边为零。
So, you must be in this case if you have a noninvertible system where the right hand side is zero.
否则，此线性方程组无解，或者无穷解？
Otherwise, well, AX equals B has either no solution, or infinitely many solutions. Yes?
记住，线性方程组问题，可以理解为求三个平面的交，因为每个方程就是一个平面。
So, remember, in the linear system, you can think of a linear system as asking you to find the intersection between three planes because each equation is the equation of a plane.
有两种可能，一是方程组可逆，这就是一般情况了，这时三个平面交于一点。
And then, we have two cases. So, the case where the system is invertible corresponds to the general situation where your three planes somehow all just intersect in one point.
把姿态信息载入非线性方程组中，从而求得飞艇的位置信息。
Substituting the information of attitude into the nonlinear equations the position of airship was obtained.
飞行动力学研究中常遇到求解非线性代数方程组的问题。
The solution of nonlinear algebraic equations is usually met in the study of flight dynamics.
经济模型经常导致对方程组的研究。
Economic models often lead to the study of systems of equations.
本文成功地将机群计算应用到解决在电法勘探中使用有限元方法（FEM）时产生的大规模线性方程组问题。
This dissertation successfully used cluster computing for solving large-scale linear algebraic equations problems when the finite element method (FEM) is applied in electrical prospecting.
这类方法具有基数型、显式计算（无须求解方程组）及局部性等优点。
This kind of schemes has advantages such as cardinal type, explicit calculation(no need to solve system of equations) and localization.
通过两个算例验证了完全欧拉方程组的正确性。
The correctness of the complete Euler equation set is verified with two functional examples.
离散后的三对角线性代数方程组用adi方法求解。
The discretized tri-diagonal linear algebraic equations are solved with ADI method.
离散后的三对角线性代数方程组用adi方法求解。
The discretized tri-diagonal linear algebraic equations are solved with ADI method.
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