- 8.11.1: In 1 and 2, use the power method as illustrated in Example 3 to fin...
- 8.11.2: In 1 and 2, use the power method as illustrated in Example 3 to fin...
- 8.11.3: In 3-6, use the power method with scaling to find the dominant eige...
- 8.11.4: In 3-6, use the power method with scaling to find the dominant eige...
- 8.11.5: In 3-6, use the power method with scaling to find the dominant eige...
- 8.11.6: In 3-6, use the power method with scaling to find the dominant eige...
- 8.11.7: In 7-10, use the method of deflation to find the eigenvalues of the...
- 8.11.8: In 7-10, use the method of deflation to find the eigenvalues of the...
- 8.11.9: In 7-10, use the method of deflation to find the eigenvalues of the...
- 8.11.10: In 7-10, use the method of deflation to find the eigenvalues of the...
- 8.11.11: In 11 and 12, use the inverse power method to find the eigenvalue o...
- 8.11.12: In 11 and 12, use the inverse power method to find the eigenvalue o...
- 8.11.13: In Example 4 of Section 3.9 we saw that the deflection curve of a t...
- 8.11.14: Suppose the column in is tapered so that the moment of inertia of a...
- 8.11.15: In Section 8.9 we saw how to compute a power Am for an n X n matrix...
Solutions for Chapter 8.11: Approximation of Eigenvalues
Full solutions for Advanced Engineering Mathematics | 5th Edition
In hypothesis testing, a region in the sample space of the test statistic such that if the test statistic falls within it, the null hypothesis cannot be rejected. This terminology is used because rejection of H0 is always a strong conclusion and acceptance of H0 is generally a weak conclusion
Analysis of variance (ANOVA)
A method of decomposing the total variability in a set of observations, as measured by the sum of the squares of these observations from their average, into component sums of squares that are associated with speciic deined sources of variation
Asymptotic relative eficiency (ARE)
Used to compare hypothesis tests. The ARE of one test relative to another is the limiting ratio of the sample sizes necessary to obtain identical error probabilities for the two procedures.
Average run length, or ARL
The average number of samples taken in a process monitoring or inspection scheme until the scheme signals that the process is operating at a level different from the level in which it began.
In experimental design, a group of experimental units or material that is relatively homogeneous. The purpose of dividing experimental units into blocks is to produce an experimental design wherein variability within blocks is smaller than variability between blocks. This allows the factors of interest to be compared in an environment that has less variability than in an unblocked experiment.
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.
Any test of signiicance based on the chi-square distribution. The most common chi-square tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data
A subset selected without replacement from a set used to determine the number of outcomes in events and sample spaces.
When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.
See Control chart.
Cumulative sum control chart (CUSUM)
A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t
A matrix that provides the tests that are to be conducted in an experiment.
Discrete uniform random variable
A discrete random variable with a inite range and constant probability mass function.
Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.
An analysis of how the variance of the random variable that represents that output of a system depends on the variances of the inputs. A formula exists when the output is a linear function of the inputs and the formula is simpliied if the inputs are assumed to be independent.
Estimator (or point estimator)
A procedure for producing an estimate of a parameter of interest. An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest.
A type of experimental design in which every level of one factor is tested in combination with every level of another factor. In general, in a factorial experiment, all possible combinations of factor levels are tested.
A signal from a control chart when no assignable causes are present
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on
The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .