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Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
In numerical linear algebra, the tridiagonal matrix algorithm, also known as the Thomas algorithm (named after Llewellyn Thomas), is a simplified form of Gaussian elimination that can be used to solve tridiagonal systems of equations. A tridiagonal system for n unknowns may be written as
First, you have to understand the problem. [2] After understanding, make a plan. [3] Carry out the plan. [4] Look back on your work. [5] How could it be better? If this technique fails, Pólya advises: [6] "If you cannot solve the proposed problem, try to solve first some related problem. Could you imagine a more accessible related problem?"
In mathematics, divided differences is an algorithm, historically used for computing tables of logarithms and trigonometric functions. [citation needed] Charles Babbage's difference engine, an early mechanical calculator, was designed to use this algorithm in its operation.
The designers chose to address this problem with a four-step solution: 1) Introducing a compiler switch that indicates if Java 1.4 or later should be used, 2) Only marking assert as a keyword when compiling as Java 1.4 and later, 3) Defaulting to 1.3 to avoid rendering prior (non 1.4 aware code) invalid and 4) Issue warnings, if the keyword is ...
A problem is said to have a polynomial-time approximation scheme if for every multiplicative factor of the optimum worse than 1 there is a polynomial-time algorithm to solve the problem to within that factor. Unless P = NP there exist problems that are in APX but without a PTAS, so the class of problems with a PTAS is strictly contained in APX.
Traditionally, to go from PostScript to PDF, a source PostScript file (that is, an executable program) is used as the basis for generating PostScript-like PDF code (see, e.g., Adobe Distiller). This is done by applying standard compiler techniques like loop unrolling , inlining and removing unused branches, resulting in code that is purely ...
Although it is possible to get around this problem using conversion code and larger data types, it makes using Java cumbersome for handling unsigned data. While a 32-bit signed integer may be used to hold a 16-bit unsigned value losslessly, and a 64-bit signed integer a 32-bit unsigned integer, there is no larger type to hold a 64-bit unsigned ...