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The relation between local and global truncation errors is slightly different from in the simpler setting of one-step methods. For linear multistep methods, an additional concept called zero-stability is needed to explain the relation between local and global truncation errors.
The condition number of a problem is the ratio of the relative change in the solution to the relative change in the input. [3] A problem is well-conditioned if small relative changes in input result in small relative changes in the solution.
The Global Offset Table, or GOT, is a section of a computer program's (executables and shared libraries) memory used to enable computer program code compiled as an ELF file to run correctly, independent of the memory address where the program's code or data is loaded at runtime.
Example A: Find the truncation in calculating the first derivative of () = at = using a step size of = Solution: The first derivative of () = is ′ =, and at = ...
In general, a method with (+) LTE (local truncation error) is said to be of kth order. The region of absolute stability for the backward Euler method is the complement in the complex plane of the disk with radius 1 centered at 1, depicted in the figure. [ 4 ]
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Inline vs. prologue – an inline comment follows code on the same line and a prologue comment precedes program code to which it pertains; line or block comments can be used as either inline or prologue
In simple cases like in the example above, programmers may manually eliminate the duplicate expressions while writing the code. The greatest source of CSEs are intermediate code sequences generated by the compiler, such as for array indexing calculations, where it is not possible for the developer to manually intervene. In some cases language ...