Low-discrepancy sequence (original) (raw)
저불일치 수열(低不一致數列, low-discrepancy sequence)은 수열의 N번째항까지의 불일치측도(discrepancy)가 작은 수열이다. 이러한 수열을 준난수열(quasirandom sequence)라고도 한다. 준난수를 일반적인 난수나 의사 난수 대신 사용하면 수치적분 성능이 개선된다.
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| dbo:abstract | En el ámbito de las matemáticas, se denomina sucesión de baja discrepancia a una sucesión con la propiedad de que para todos los valores de N, su subsucesión x 1, ..., x N tiene una baja. En términos generales, la discrepancia de una sucesión es baja si la proporción de puntos en la sucesión que se encuentran en un conjunto arbitrario B es casi proporcional a la medida de B , como sucedería en promedio (pero no para muestras particulares) en el caso de un distribución uniforme. Las definiciones específicas de discrepancia difieren en cuanto a la elección de B y cómo se calcula (por lo general normalizada) la discrepancia para cada B y como se combina la discrepancia (normalmente tomando el peor valor). Las sucesiones de baja discrepancia también se llaman sucesiones cuasi-aleatorias o sub-aleatorias, debido a ser usadas comúnmente como reemplazo de números aleatorios uniformemente distribuidos.El calificador "cuasi" se utiliza para indicar más claramente que los valores de una sucesión de baja discrepancia no son aleatorios ni pseudoaleatorios, pero tales sucesiones comparten algunas de las propiedades de las variables aleatorias y en ciertas aplicaciones tales como el su baja discrepancia es una ventaja importante. (es) In mathematics, a low-discrepancy sequence is a sequence with the property that for all values of N, its subsequence x1, ..., xN has a low discrepancy. Roughly speaking, the discrepancy of a sequence is low if the proportion of points in the sequence falling into an arbitrary set B is close to proportional to the measure of B, as would happen on average (but not for particular samples) in the case of an equidistributed sequence. Specific definitions of discrepancy differ regarding the choice of B (hyperspheres, hypercubes, etc.) and how the discrepancy for every B is computed (usually normalized) and combined (usually by taking the worst value). Low-discrepancy sequences are also called quasirandom sequences, due to their common use as a replacement of uniformly distributed random numbers.The "quasi" modifier is used to denote more clearly that the values of a low-discrepancy sequence are neither random nor pseudorandom, but such sequences share some properties of random variables and in certain applications such as the quasi-Monte Carlo method their lower discrepancy is an important advantage. (en) En mathématiques, une suite à discrépance faible est une suite ayant la propriété que pour tout entier N, la sous-suite x1, ..., xN a une basse. Dans les faits, la discrépance d'une suite est faible si la proportion des points de la suite sur un ensemble B est proche de la valeur de la mesure de B, ce qui est le cas en moyenne (mais pas pour des échantillons particuliers) pour une suite équidistribuée. Plusieurs définitions de la discrépance existent selon la forme de B (hypersphères, hypercubes, etc.) et la méthode de calcul de la discrépance sur B. Les suites à discrépance faible sont appelées quasi aléatoires ou sous-aléatoires, en raison de leur utilisation pour remplacer les tirages de la loi uniforme continue.Le préfixe « quasi » précise ainsi que les valeurs d'une suite à discrépance faible ne sont pas aléatoires ou pseudo-aléatoires, mais ont des propriétés proches de tels tirages, permettant ainsi leur usage intéressant dans la méthode de quasi-Monte-Carlo. (fr) 저불일치 수열(低不一致數列, low-discrepancy sequence)은 수열의 N번째항까지의 불일치측도(discrepancy)가 작은 수열이다. 이러한 수열을 준난수열(quasirandom sequence)라고도 한다. 준난수를 일반적인 난수나 의사 난수 대신 사용하면 수치적분 성능이 개선된다. (ko) |
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| rdfs:comment | 저불일치 수열(低不一致數列, low-discrepancy sequence)은 수열의 N번째항까지의 불일치측도(discrepancy)가 작은 수열이다. 이러한 수열을 준난수열(quasirandom sequence)라고도 한다. 준난수를 일반적인 난수나 의사 난수 대신 사용하면 수치적분 성능이 개선된다. (ko) En el ámbito de las matemáticas, se denomina sucesión de baja discrepancia a una sucesión con la propiedad de que para todos los valores de N, su subsucesión x 1, ..., x N tiene una baja. En términos generales, la discrepancia de una sucesión es baja si la proporción de puntos en la sucesión que se encuentran en un conjunto arbitrario B es casi proporcional a la medida de B , como sucedería en promedio (pero no para muestras particulares) en el caso de un distribución uniforme. Las definiciones específicas de discrepancia difieren en cuanto a la elección de B y cómo se calcula (por lo general normalizada) la discrepancia para cada B y como se combina la discrepancia (normalmente tomando el peor valor). (es) In mathematics, a low-discrepancy sequence is a sequence with the property that for all values of N, its subsequence x1, ..., xN has a low discrepancy. Roughly speaking, the discrepancy of a sequence is low if the proportion of points in the sequence falling into an arbitrary set B is close to proportional to the measure of B, as would happen on average (but not for particular samples) in the case of an equidistributed sequence. Specific definitions of discrepancy differ regarding the choice of B (hyperspheres, hypercubes, etc.) and how the discrepancy for every B is computed (usually normalized) and combined (usually by taking the worst value). (en) En mathématiques, une suite à discrépance faible est une suite ayant la propriété que pour tout entier N, la sous-suite x1, ..., xN a une basse. Dans les faits, la discrépance d'une suite est faible si la proportion des points de la suite sur un ensemble B est proche de la valeur de la mesure de B, ce qui est le cas en moyenne (mais pas pour des échantillons particuliers) pour une suite équidistribuée. Plusieurs définitions de la discrépance existent selon la forme de B (hypersphères, hypercubes, etc.) et la méthode de calcul de la discrépance sur B. (fr) |
| rdfs:label | Sucesión de baja discrepancia (es) Suite à discrépance faible (fr) Low-discrepancy sequence (en) 저불일치 수열 (ko) |
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