Concepts inA Parallel Method for Tridiagonal Equations
Tridiagonal matrix
In linear algebra, a tridiagonal matrix is a matrix that has nonzero elements only in the main diagonal, the first diagonal below this, and the first diagonal above the main diagonal. For example, the following matrix is tridiagonal: The determinant of a tridiagonal matrix is given by a continuant of its elements. Determining an orthogonal transformation to tridiagonal form can be done with the Lanczos algorithm.
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Parallel computing
Parallel computing is a form of computation in which many calculations are carried out simultaneously, operating on the principle that large problems can often be divided into smaller ones, which are then solved concurrently ("in parallel"). There are several different forms of parallel computing: bit-level, instruction level, data, and task parallelism.
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Equation
An equation is a mathematical statement that asserts the equality of two expressions. In modern notation, this is written by placing the expressions on either side of an equals sign (=), for example asserts that x+3 is equal to 5. The = symbol was invented by Robert Recorde (1510¿), who considered that nothing could be more equal than parallel straight lines with the same length.
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