Numerical methods for linear least squaresNumerical methods for linear least squares entails the numerical analysis of linear least squares problems. A general approach to the least squares problem can be described as follows. Suppose that we can find an n by m matrix S such that XS is an orthogonal projection onto the image of X. Then a solution to our minimization problem is given by simply because is exactly a sought for orthogonal projection of onto an image of X (see the picture below and note that as explained in the next section the image of X is just a subspace generated by column vectors of X).
Numerical stabilityIn the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues.
Cutting fluidCutting fluid is a type of coolant and lubricant designed specifically for metalworking processes, such as machining and stamping. There are various kinds of cutting fluids, which include oils, oil-water emulsions, pastes, gels, aerosols (mists), and air or other gases. Cutting fluids are made from petroleum distillates, animal fats, plant oils, water and air, or other raw ingredients. Depending on context and on which type of cutting fluid is being considered, it may be referred to as cutting fluid, cutting oil, cutting compound, coolant, or lubricant.
Evolutionary algorithmIn computational intelligence (CI), an evolutionary algorithm (EA) is a subset of evolutionary computation, a generic population-based metaheuristic optimization algorithm. An EA uses mechanisms inspired by biological evolution, such as reproduction, mutation, recombination, and selection. Candidate solutions to the optimization problem play the role of individuals in a population, and the fitness function determines the quality of the solutions (see also loss function).
Spinal cord injuryA spinal cord injury (SCI) is damage to the spinal cord that causes temporary or permanent changes in its function. Symptoms may include loss of muscle function, sensation, or autonomic function in the parts of the body served by the spinal cord below the level of the injury. Injury can occur at any level of the spinal cord and can be complete, with a total loss of sensation and muscle function at lower sacral segments, or incomplete, meaning some nervous signals are able to travel past the injured area of the cord up to the Sacral S4-5 spinal cord segments.
Ultrasonic testingUltrasonic testing (UT) is a family of non-destructive testing techniques based on the propagation of ultrasonic waves in the object or material tested. In most common UT applications, very short ultrasonic pulse-waves with center frequencies ranging from 0.1-15 MHz, and occasionally up to 50 MHz, are transmitted into materials to detect internal flaws or to characterize materials. A common example is ultrasonic thickness measurement, which tests the thickness of the test object, for example, to monitor pipework corrosion.
Genetic programmingIn artificial intelligence, genetic programming (GP) is a technique of evolving programs, starting from a population of unfit (usually random) programs, fit for a particular task by applying operations analogous to natural genetic processes to the population of programs. The operations are: selection of the fittest programs for reproduction (crossover), replication and/or mutation according to a predefined fitness measure, usually proficiency at the desired task.
Finite element methodThe finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems).
DesignA design is a concept of either an object, a process, or a system that is specific and, in most cases, detailed. Design refers to something that is or has been intentionally created by a thinking agent, though it is sometimes used to refer to the nature of something. The verb to design expresses the process of developing a design. In some cases, the direct construction of an object without an explicit prior plan may also be considered to be a design (such as in some artwork and craftwork).
Particle swarm optimizationIn computational science, particle swarm optimization (PSO) is a computational method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality. It solves a problem by having a population of candidate solutions, here dubbed particles, and moving these particles around in the search-space according to simple mathematical formula over the particle's position and velocity.
Electromagnetic acoustic transducerElectromagnetic acoustic transducer (EMAT) is a transducer for non-contact acoustic wave generation and reception in conducting materials. Its effect is based on electromagnetic mechanisms, which do not need direct coupling with the surface of the material. Due to this couplant-free feature, EMATs are particularly useful in harsh, i.e., hot, cold, clean, or dry environments. EMATs are suitable to generate all kinds of waves in metallic and/or magnetostrictive materials.
Intervertebral discAn intervertebral disc (or intervertebral fibrocartilage) lies between adjacent vertebrae in the vertebral column. Each disc forms a fibrocartilaginous joint (a symphysis), to allow slight movement of the vertebrae, to act as a ligament to hold the vertebrae together, and to function as a shock absorber for the spine. Intervertebral discs consist of an outer fibrous ring, the anulus fibrosus disci intervertebralis, which surrounds an inner gel-like center, the nucleus pulposus.
