3.4.2 Norms of Matrices.
As with vectors, a norm of a matrix A is a numerical measure of its size. However, now we are also
interested in the effect of the matrix A on a vector x when we form y = Ax.
3
Systems of Equations
3.1 Systems of equations
3.1.1 Notation and Examples
In this chapter we look at algorithms to solve systems of equations. A system of n linear equations with n
unknowns can be w
3.2 Gaussian Elimination Without Pivoting.
Gaussian elimination is one popular procedure to solve linear equations. As we shall see, it leads to a
decomposition of the coefficient matrix A as the prod
3.3 Gaussian Elimination With Partial Pivoting.
In the previous section we discussed Gaussian elimination. In that discussion we used equation 1 to
eliminate x1 from equations 2 through n. Then we use
4.2 Divided differences.
In section 4.1 we considered two methods for constructing an nth degree polynomial
(1)
y = a0 + a1x + a2x2 + a3x3 +
+ anxn
that passes through n + 1 points
(2)
(x0, y0), (x1,
2
Nonlinear Equations
This chapter is concerned with approximating the solution of a single nonlinear equation. We begin with
general principles involved in the solution of nonlinear equations such as
3.4.4 Propagation of errors in linear formulas componentwise analysis.
In this section we look at the propagation of errors in linear formulas by treating the errors component-wise.
This is more preci
4
Approximation
Approximation is concerned with finding functions y = f(x) that either approximate other functions or
experimental data. In the first case we want to approximate a given function by a
3.4.1 Norms of Vectors.
In this and the next two sections we look at the propagation of errors in linear formulas using vector and
matrix norms. Although this does not give as precise a result as when
4.3 The Error in the Interpolating Polynomial.
In this section we derive a formula for the error in the interpolating polynomial when it is used to
approximate a given function. In this section we ass
Exam 1
Math 472/572
Fall 2010
Name: _ This is a closed book exam. You may use a calculator and the
formulas handed out along with the exam. Show your work so I can see how you arrived at your
answers.