Concepts inHow to vectorize the algebraic multilevel iteration
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex analysis, topology and number theory.
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Vectorization (image tracing)
In computer graphics, vectorization refers to the process of converting raster graphics into vector graphics.
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Array programming
In computer science, array programming languages (also known as vector or multidimensional languages) generalize operations on scalars to apply transparently to vectors, matrices, and higher dimensional arrays. Array programming primitives concisely express broad ideas about data manipulation. The level of conciseness can be dramatic in certain cases: it is not uncommon to find array programming language one-liners that require more than a couple of pages of Java code.
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System of linear equations
In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables. For example, is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of numbers to the variables such that all the equations are simultaneously satisfied. A solution to the system above is given by since it makes all three equations valid.
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Matrix multiplication
In mathematics, matrix multiplication is a binary operation that takes a pair of matrices, and produces another matrix. This term may refer to a number of different ways to multiply matrices, but most commonly refers to the matrix product. This article will use the following notational conventions. Matrices are represented by capital letters in bold, vectors in lowercase bold, and entries of vectors and matrices are italic (since they are scalars).
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Vector processor
A vector processor, or array processor, is a central processing unit (CPU) that implements an instruction set containing instructions that operate on one-dimensional arrays of data called vectors. This is in contrast to a scalar processor, whose instructions operate on single data items.
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Finite difference
A finite difference is a mathematical expression of the form f(x + b) ¿ f(x + a). If a finite difference is divided by b ¿ a, one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems. Recurrence relations can be written as difference equations by replacing iteration notation with finite differences.
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Fujitsu
is a Japanese multinational information technology equipment and services company headquartered in Tokyo, Japan. It is the world's third-largest IT services provider measured by revenues. Fujitsu's chiefly makes computing products, but the company and its subsidiaries also offer a diversity of products and services in the areas of personal computing, telecommunications and advanced microelectronics.
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