澄清求解2*2实矩阵特征向量时机器ε的影响

代码来自函数 eigen2x2

double u = (a + c)*0.5;
double v = std::sqrt((a - c)*(a - c)*0.25 + b*b);
double l1 = u + v; //the 1st eigenvalue
double l2 = u - v; // the 2nd eigenvalue

l1 ,这意味着解决以下系统:

eigen2x2 详情如下:

        double x = b;
        double y = l1 - a;
        double e = fabs(x);

        if (e + fabs(y) < 1e-4)
        {
            y = b;
            x = l1 - c;
            e = fabs(x);
            if (e + fabs(y) < 1e-4)
            {
                e = 1. / (e + fabs(y) + FLT_EPSILON);
                x *= e, y *= e;
            }
        }

        double d = 1. / std::sqrt(x*x + y*y + DBL_EPSILON);
        double x1 = x*d; //I moderately changed variable name for simplicity.
        double x2 = y*d;   

哪里 x1 和 x2 构造对应于 .

问题

        e = 1. / (e + fabs(y) + FLT_EPSILON);
        x *= e, y *= e;

那么它扮演的角色是什么呢?允许踢出去吗 FLT_EPSILON DBL_EPSILON ?