Concepts inSolving narrow banded systems on ensemble architectures
Gaussian elimination
In linear algebra, Gaussian elimination is an algorithm for solving systems of linear equations. It can also be used to find the rank of a matrix, to calculate the determinant of a matrix, and to calculate the inverse of an invertible square matrix. The method is named after Carl Friedrich Gauss, but it was not invented by him. Elementary row operations are used to reduce a matrix to what is called triangular form (in numerical analysis) or row echelon form (in abstract algebra).
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Triangular matrix
In the mathematical discipline of linear algebra, a triangular matrix is a special kind of square matrix. A square matrix is called lower triangular if all the entries above the main diagonal are zero. Conversely a square matrix is called upper triangular if all the entries below the main diagonal are zero. A triangular matrix is one that is either lower triangular or upper triangular. A matrix that is both upper and lower triangular is a diagonal matrix.
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Block matrix
In the mathematical discipline of matrix theory, a block matrix or a partitioned matrix is a matrix broken into sections called blocks. Looking at it another way, the matrix is written in terms of smaller matrices. We group the rows and columns into adjacent 'bunches'. A partition is the rectangle described by one bunch of adjacent rows and one bunch of adjacent columns.
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Binary tree
In computer science, a binary tree is a tree data structure in which each node has at most two child nodes, usually distinguished as "left" and "right". Nodes with children are parent nodes, and child nodes may contain references to their parents. Outside the tree, there is often a reference to the "root" node (the ancestor of all nodes), if it exists. Any node in the data structure can be reached by starting at root node and repeatedly following references to either the left or right child.
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Parallel algorithm
In computer science, a parallel algorithm or concurrent algorithm, as opposed to a traditional sequential (or serial) algorithm, is an algorithm which can be executed a piece at a time on many different processing devices, and then put back together again at the end to get the correct result. Some algorithms are easy to divide up into pieces like this.
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Array data structure
In computer science, an array data structure or simply array is a data structure consisting of a collection of elements, each identified by at least one array index or key. An array is stored so that the position of each element can be computed from its index tuple by a mathematical formula.
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Arithmetic
Arithmetic or arithmetics is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of operations that combine numbers. In common usage, it refers to the simpler properties when using the traditional operations of addition, subtraction, multiplication and division with smaller values of numbers.
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Variable (mathematics)
In mathematics, a variable is a value that may change within the scope of a given problem or set of operations. In contrast, a constant is a value that remains unchanged, though often unknown or undetermined. The concepts of constants and variables are fundamental to many areas of mathematics and its applications. A "constant" in this context should not be confused with a mathematical constant which is a specific number independent of the scope of the given problem.
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