一、填空题 （每题 1．5 分，共 24 分） 1．(30)10 = （ ）2 ＝（ ）16 2.（00110100）8421BCD ＝（ ）10＝（ ）2

4.1 引言 4.2 经典谱估计 4.3 现代谱估计中的参数建模 4.4 AR模型谱估计的性质 4.5 AR谱估计的方法 4.6 最大熵谱估计与最大似然谱估计 4.7 特征分解法谱估计

麻省理工学院：偏微分方程式数字方法（英文版）_lec26

Outline Reminder about 1-D 1st and 2nd Kind egns Three-D Laplace Problems Interior Neumann Problem Null space issue First Kind Theory for 3-D Laplace Informal Convergence Theory

Goals Theory A priori A priori error estimates N1 bound various“ measures” of u exact]-un [approximate] in terms of C(n, problem parameters h [mesh diameter, and u

1 Model problem 1.1 Formulations 1.1.1 Strong formulation LIDE Find a such that for Q a polygonal domain Generalizat ion We look here at a particularly simple but nevertheless illustrative problem

Outline Easy technique for computing integrals Piecewise constant approach Gaussian Quadrature Convergence properties Essential role of orthogonal polynomials Multidimensional Integrals Techniques for singular kernels Adaptation and variable transformation Singular quadrature

Integral Equation Methods Reminder about Galerkin and collocation Example of convergence issues in 1D First and second kind integral equations Develop some intuition about the difficulties Convergence for second kind equations Consistency and stability issues Nystrom Method

Integral Equation Methods Reminder about galerkin and Collocation Example of convergence issues in 1D First and second kind integral equations Develop some intuition about the difficulties Convergence for second kind equations Consistency and stability issues

1 Scalar Conservation laws 1.1 Definit 1.1.1 Conservative form