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Algorithm in numerical analysis
Miller's recurrence algorithm is a procedure for the backward calculation of a rapidly decreasing solution of a three-term recurrence relation developed
Miller's_recurrence_algorithm
Pattern defining an infinite sequence of numbers
In mathematics, a recurrence relation is an equation according to which the n {\displaystyle n} th term of a sequence of numbers is equal to some combination
Recurrence_relation
{\displaystyle y_{0},y_{1}} . Miller's recurrence algorithm Walter Gautschi. Computational Aspects of Three-Term Recurrence Relations. SIAM Review, 9:24–80
Three-term recurrence relation
Three-term_recurrence_relation
Divide and conquer sorting algorithm
made by the algorithm (Cormen et al., Introduction to Algorithms, Section 7.3). Three common proofs of this claim use percentiles, recurrences, and binary
Quicksort
Algorithm for integer multiplication
The Karatsuba algorithm is a fast multiplication algorithm for integers. It was discovered by Anatoly Karatsuba in 1960 and published in 1962. It is a
Karatsuba_algorithm
Algorithm for computing greatest common divisors
In mathematics, the Euclidean algorithm, or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers
Euclidean_algorithm
Mathematical algorithm
algorithm can be quadratic under certain regularity conditions. In general (under weaker conditions), the convergence rate is linear. The recurrence relation
Gauss–Newton_algorithm
Prime-counting algorithm
The Meissel–Lehmer algorithm (after Ernst Meissel and Derrick Henry Lehmer) is an algorithm that computes exact values of the prime-counting function.
Meissel–Lehmer_algorithm
Algorithm to multiply matrices
divide-and-conquer recurrences shows this recursion to have the solution Θ(n3), the same as the iterative algorithm. A variant of this algorithm that works for
Matrix multiplication algorithm
Matrix_multiplication_algorithm
Method for division with remainder
A division algorithm is an algorithm which, given two integers N and D (respectively the numerator and the denominator), computes their quotient and/or
Division_algorithm
British mathematician and computing pioneer (1906–1981)
proposal of certain algorithms. Miller's recurrence algorithm is mentioned in the Handbook of Mathematical Functions. What Miller perceived was that in
J._C._P._Miller
Method for computing the relation of two integers with their greatest common divisor
and computer programming, the extended Euclidean algorithm is an extension to the Euclidean algorithm, and computes, in addition to the greatest common
Extended_Euclidean_algorithm
Algorithm for generating pseudo-randomized numbers
A linear congruential generator (LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear
Linear_congruential_generator
Doubly exponential integer sequence
converges to 1 more rapidly than any other series of unit fractions. The recurrence by which it is defined allows the numbers in the sequence to be factored
Sylvester's_sequence
Product of numbers from 1 to n
formula or recurrence is not efficient, faster algorithms are known, matching to within a constant factor the time for fast multiplication algorithms for numbers
Factorial
Rational number sequence
describes an algorithm for generating Bernoulli numbers with Babbage's machine; it is disputed whether Lovelace or Babbage developed the algorithm. As a result
Bernoulli_number
Mathematical puzzle game
produced solution is the only one with this minimum number of moves. Using recurrence relations, the exact number of moves that this solution requires can be
Tower_of_Hanoi
Greatest integer less than or equal to square root
y {\displaystyle y} and k {\displaystyle k} be non-negative integers. Algorithms that compute (the decimal representation of) y {\displaystyle {\sqrt {y}}}
Integer_square_root
Seminumerical Algorithms, 3rd ed., Addison Wesley Longman (1998); See pag. 27. Tausworthe, R. C. (1965). "Random Numbers Generated by Linear Recurrence Modulo
List of random number generators
List_of_random_number_generators
Special-purpose integer factorization algorithm
number field sieve (SNFS) is a special-purpose integer factorization algorithm. The general number field sieve (GNFS) was derived from it. The special
Special_number_field_sieve
Exponential function of an exponential function
of algorithms, double exponential sequences are used within the design of an algorithm rather than in its analysis. An example is Chan's algorithm for
Double_exponential_function
Branch of machine learning
transform the data into a more suitable representation for a classification algorithm to operate on. In the deep learning approach, features are not hand-crafted
Deep_learning
Arithmetic operation, inverse of nth power
x0, which is also a positive real number, and then iterates using the recurrence relation x k + 1 = x k − x k n − A n x k n − 1 {\displaystyle x_{k+1}=x_{k}-{\frac
Nth_root
Theory', 'The X Factor' & 'Glee' Adjusted Up; 'The Vampire Diaries' & 'The Millers' Adjusted Down". TV by the Numbers. Archived from the original on October
List of The Big Bang Theory episodes
List_of_The_Big_Bang_Theory_episodes
Test if a Mersenne number is prime
odd prime. The primality of p can be efficiently checked with a simple algorithm like trial division since p is exponentially smaller than Mp. Define a
Lucas–Lehmer_primality_test
Random process independent of past history
and null recurrent otherwise. Periodicity, transience, recurrence and positive and null recurrence are class properties — that is, if one state has the
Markov_chain
Decomposition of an integer as a sum of positive integers
it has both asymptotic expansions that accurately approximate it and recurrence relations by which it can be calculated exactly. It grows as an exponential
Integer_partition
Pseudorandom number generator
It is a linear congruential generator (LCG) of the Park–Miller type defined by the recurrence V j + 1 = 65539 ⋅ V j mod 2 31 {\displaystyle V_{j+1}=65539\cdot
RANDU
Class of artificial neural network
years, transformers, which rely on self-attention mechanisms instead of recurrence, have become the dominant architecture for many sequence-processing tasks
Recurrent_neural_network
Types of special mathematical functions
that the real part of s is positive. By integration by parts we find the recurrence relations Γ ( s + 1 , x ) = s Γ ( s , x ) + x s e − x {\displaystyle \Gamma
Incomplete_gamma_function
Probability distribution
converge for all real and complex values of x {\displaystyle x} . The recurrence relation for Hermite polynomials Hen(x) may be used to efficiently construct
Normal_distribution
Number sequence 3,0,2,3,2,5,5,7,10,...
numbers do to the Fibonacci sequence. The Perrin numbers are defined by the recurrence relation P ( 0 ) = 3 , P ( 1 ) = 0 , P ( 2 ) = 2 , P ( n ) = P ( n − 2
Perrin_number
On tangency patterns of circles
577–606, doi:10.1215/ijm/1255987673 Benjamini, Itai; Schramm, Oded (2001), "Recurrence of distributional limits of finite planar graphs", Electronic Journal
Circle_packing_theorem
Mathematical sequences
sequence from left to right, one uses recurrence (1). Traversing the sequence from right to left, one uses the recurrence T n = T n + 3 − T n + 2 − T n + 1
Generalizations of Fibonacci numbers
Generalizations_of_Fibonacci_numbers
Proof that a number is prime
multiplication, this is only O((log n)4) time; using the multiplication algorithm with best-known asymptotic running time, due to David Harvey and Joris
Primality_certificate
Branch of statistics
censoring time Event (recurrence of aml cancer) is indicated by the variable "status". 0 = no event (censored), 1 = event (recurrence) Treatment group: the
Survival_analysis
Field of electrical engineering
Processing: Data Science, Algorithms, and Computational Statistics. OUP Oxford. ISBN 978-0-19-102431-3. Steven B. Damelin; Willard Miller, Jr (2012). The Mathematics
Signal_processing
Drug mixture used mainly to treat ADHD and narcolepsy
result in withdrawal symptoms. Discontinuation of amphetamine may cause a recurrence of ADHD symptoms due to the cessation of treatment-related drug effects
Adderall
Cancer originating in or on the ovary
5 years, 20% of stage I and II cancers recur. Most recurrences are in the abdomen. If a recurrence occurs in advanced disease, it typically occurs within
Ovarian_cancer
Aspect of music
of opposite or different conditions". This general meaning of regular recurrence or pattern in time can apply to a wide variety of cyclical natural phenomena
Rhythm
Chronic multi-symptomatic pain disorder
Biography, Statistics, & Facts | Britannica". Encyclopedia Britannica. "Recurrence of Fibrositis Keeps Bradman Out of Cricket". Mercury. 2 March 1946. p
Fibromyalgia
Probability distribution and special case of gamma distribution
2 {\textstyle f(x;\,2)={\frac {1}{2}}e^{-x/2}} directly. The integer recurrence of the gamma function makes it easy to compute F ( x ; k ) {\displaystyle
Chi-squared_distribution
Unique positive real number which when multiplied by itself gives 2
There are many algorithms for approximating 2 {\displaystyle {\sqrt {2}}} as a ratio of integers or as a decimal. The most common algorithm for this, which
Square_root_of_2
Genetic disorder
all races, its association with older maternal age, and its rarity of recurrence had been noticed. Medical texts had assumed it was caused by a combination
Down_syndrome
Medication for pain and fever
Against Rheumatism (EULAR) for hand osteoarthritis. Similarly, the ESCEO algorithm for the treatment of knee osteoarthritis recommends limiting the use of
Paracetamol
leading Ohno to state that the "...all-pervasive principle of repetitious recurrence governs not only coding sequence construction but also human endeavor
Protein_music
Group of neurological disorders causing seizures
if clinical evidence suggests a high risk of recurrence. Isolated seizures that occur without recurrence risk or are provoked by identifiable causes are
Epilepsy
Medical classification system
treated with less aggressive treatments, such as lumpectomy. Treatment algorithms rely on breast cancer classification to define specific subgroups that
Breast_cancer_classification
Generalized sphere of dimension n (mathematics)
{\displaystyle S_{0}=2} , V 1 = 2 {\displaystyle V_{1}=2} from above, these recurrences can be used to compute the surface area of any sphere or volume of any
N-sphere
CNS stimulant and isomer of amphetamine
result in withdrawal symptoms. Discontinuation of amphetamine may cause a recurrence of ADHD symptoms due to the cessation of treatment-related drug effects
Dextroamphetamine
Illegal attempt to unseat an incumbent
Jessica Maves; Sudduth, Jun Koga (January 2016). "Military purges and the recurrence of civil conflict". Research & Politics. 3 (1) 2053168016630730. doi:10
Coup_d'état
Disease that damages the myelin sheaths around nerves
benefit for people with MS; this includes for measures such as relapse recurrence, disability, and MRI lesions while effects on health‐related quality of
Multiple_sclerosis
pleasant or unpleasant) and how it ended. Persistence: The unwanted recurrence of memories of a traumatic event. The Perky effect, where real images
List_of_cognitive_biases
Central nervous system stimulant
result in withdrawal symptoms. Discontinuation of amphetamine may cause a recurrence of ADHD symptoms due to the cessation of treatment-related drug effects
Amphetamine
Number, approximately 1.618
\end{aligned}}} Successive powers of the golden ratio obey the Fibonacci recurrence, φ n + 1 = φ n + φ n − 1 {\displaystyle \textstyle \varphi ^{n+1}=\varphi
Golden_ratio
Sudden or unexpected loss of heartbeat
cardiac defibrillator may be considered to reduce the chance of death from recurrence. Per the 2015 American Heart Association Guidelines, there were approximately
Cardiac_arrest
Type of cancer in animals
loss of appetite, weight loss, and fatigue. Due to the high risk of recurrence and ensuing problems, close monitoring of dogs undergoing chemotherapy
Lymphoma_in_animals
Benzodiazepine sedative
febrile seizures that may occur in children under five years of age. Recurrence rates are reduced, but side effects are common, and the decision to treat
Diazepam
Borůvka's algorithm, an algorithm for finding a minimum spanning tree in a graph, was first published in 1926 by Otakar Borůvka. The algorithm was rediscovered
List_of_multiple_discoveries
Class of CNS depressant drugs
clinical experience supports continuing benzodiazepine treatment to prevent recurrence. Although major concerns about benzodiazepine tolerance and withdrawal
Benzodiazepine
Process to identify a disease or disorder
useful to optimize treatment, further specify the prognosis or prevent recurrence of the disease or condition in the future.[citation needed] The initial
Medical_diagnosis
Collection of random variables
Elements of Queueing Theory: Palm Martingale Calculus and Stochastic Recurrences. Springer Science & Business Media. ISBN 978-3-662-11657-9. P. Hall;
Stochastic_process
Random matrix with gaussian entries
}}}} Using the confluent form of Christoffel–Darboux and the three-term recurrence of Hermite polynomials, the spectral density of GUE(N) for finite values
Gaussian_ensemble
Area of body discomfort
walking and education intervention for the prevention of low back pain recurrence in Australia (WalkBack): a randomised controlled trial". The Lancet. 404
Back_pain
(computational complexity theory) Master theorem (analysis of algorithms) (recurrence relations, asymptotic analysis) Max/min_CSP/Ones_classification_theorems
List_of_theorems
Medical area for women's reproductive health
cancer treatment, assisting with earlier detection and predicting disease recurrence. In terms of surgery, research has led to minimally invasive approaches
Gynaecology
Form of kidney cancer
(2011). "Reactive Hypertrophy of an Accessory Spleen Mimicking Tumour Recurrence of Metastatic Renal Cell Carcinoma". Asian Journal of Surgery. 34 (1):
Renal_cell_carcinoma
walking programs as a cost-effective method against lower back pain recurrence (19 June). Hazard research is published: a study finds toxic metals including
2024_in_science
Class of medications
mucopeptide biosynthesis, leading to bacterial death. This can reduce the ulcer recurrence risk. Amoxicillin may cause gastrointestinal discomfort, namely nausea
Anti-ulcer_agent
Structure at the rear of the vertebrate brain, beneath the cerebrum
with very little recurrent internal transmission. The small amount of recurrence that does exist consists of mutual inhibition; there are no mutually excitatory
Cerebellum
Diplomatic policy of concessions
Violent Conflict? Post-Conflict Government Policy and Two Types of Conflict Recurrence". Defence and Peace Economics. 36 (2): 200–226. doi:10.1080/10242694.2024
Appeasement
American geneticist
Detection of Circulating Tumor DNA Antedates Breast Cancer Metastatic Recurrence. Clinical Cancer Research. 2019;25(14):4255-4263. Halloran PF, Reeve J
Paul_Billings
phase I trialed personalized mRNA vaccine against pancreatic cancer recurrence (10 May), a novel antibiotic (Streptothricin F) against ABR bacteria (9
2023_in_science
Field in social science
Capitalist peace Democratic peace theory Global Peace Index Historic recurrence International security Just war theory List of peace activists Nonkilling
Peace_and_conflict_studies
Human viral infection
investigate the role of the preventive antiviral medication against HCV recurrence after transplantation. One barrier to finding treatments for hepatitis
Hepatitis_C
Therapy using ionizing radiation, usually to treat cancer
parts. It may also be used as part of adjuvant therapy, to prevent tumor recurrence after surgery to remove a primary malignant tumor (for example, early
Radiation_therapy
American music theorist-analyst and composer
into a feedback loop involving some technical analytical procedures or algorithm, whose output is monitored and which is adjusted in response to that monitoring
Joshua_Banks_Mailman
Cell from a primary tumor carried by blood circulation
maintenance therapy Maintrac has been used experimentally to monitor cancer recurrence. Studies using Maintrac have shown that EpCAM positive cells can be found
Circulating_tumor_cell
Blood clot (thrombus) that forms within a vein
drug fondaparinux (a factor Xa inhibitor), which reduces extension and recurrence of superficial venous thrombosis as well as progression to symptomatic
Venous_thrombosis
Branch of geophysics, primarily seismology
segment, identifying these characteristic earthquakes and timing their recurrence rate (or conversely return period) should therefore inform us about the
Earthquake_prediction
portal History of science portal 2020s in science and technology Historic recurrence Historiography of science History and philosophy of science Philosophy
History_of_science
Avenue in New York City
Safety Curbs; Secondary Walls of Reinforced Concrete Expected to Prevent Recurrence of Accidents". The New York Times. May 6, 1940. ISSN 0362-4331. Archived
Riverside_Drive_(Manhattan)
Digital information reflecting an individual's karyotype
where less than 20% have tumor recurrence. 18q LOH is an established biomarker associated with high risk of tumor recurrence in stage II colon cancer. Figure
Virtual_karyotype
Israeli molecular biophysicist
PMID 2006170. Kolker, Eugene; Trifonov, Edward N. (1995). "Periodic Recurrence of Methionines: Fossil of Gene Fusion?". Proceedings of the National Academy
Edward_Trifonov
MILLERS RECURRENCE-ALGORITHM
MILLERS RECURRENCE-ALGORITHM
Surname or Lastname
English (of Norman origin) and northern French
English (of Norman origin) and northern French : habitational name from any of the numerous places in France named Viller(s) or Villier(s), from Late Latin villare ‘outlying farm’, ‘dependent settlement’.
Boy/Male
American, Australian, British, English, Latin
One who Grinds Grain; Surname
Surname or Lastname
English
English : variant spelling of Millet.Irish (mainly County Mayo) : Anglicized form of Gaelic Ó Mealóid, from an occupational or status name derived from Latin miles ‘soldier’.
Boy/Male
Czechoslovakian
Miller.
Male
English
Patronymic form of English Mile, MILES means "son of Mile."
Surname or Lastname
Respelling of German Ehlers.English
Respelling of German Ehlers.English : habitational name from High and Low Ellers in West Yorkshire, named from Old English alras, plural of alor ‘alder’.
Male
French
French name derived from Late Latin Ægidius, GILLES means "shield of goatskin."
Boy/Male
British, English, Jamaican
From Near the Mills; Mile's Son
Surname or Lastname
English and Scottish
English and Scottish : occupational name for a miller. The standard modern vocabulary word represents the northern Middle English term, an agent derivative of mille ‘mill’, reinforced by Old Norse mylnari (see Milner). In southern, western, and central England Millward (literally, ‘mill keeper’) was the usual term.Southwestern and Swiss German and Jewish (Ashkenazic) : variant of Müller (see Mueller).
Surname or Lastname
Americanized form of German Möller (see Moeller).German
Americanized form of German Möller (see Moeller).German : habitational name for someone from Melle.German, Jewish (Ashkenazic), and Polish : occupational name for a miller or flour merchant, from an agent derivative of German Mehl ‘flour’.English : variant of Miller.
Surname or Lastname
English
English : variant of Mills. Compare Milner.
Surname or Lastname
Irish
Irish : variant of Mullen.English : from Old French Milon, an inflected form of the personal name Miles (see Miles 1).English : from Middle English milne, adjectival form of mille ‘mill’, or perhaps a topographic name for someone living in a lane leading to a mill, from Middle English mille, milne ‘mill’ + lane, lone ‘lane’.Dutch : patronymic from Miele 3.
Surname or Lastname
English
English : variant spelling of Mills.
Surname or Lastname
North German and Frisian
North German and Frisian : patronymic from Hiller 3.English : variant of Hillhouse.
Boy/Male
American, Australian, British, Chinese, Christian, English, French, Jamaican
One who Grinds Grain; Guardian of the Mill; Strong; Miller; Grain Grinder
Surname or Lastname
French
French : from the Germanic personal name Milo (see Miles 1).English : variant spelling of Mill.Dutch : variant of Miele.
Surname or Lastname
English
English : variant of Guiler.German : variant of Gille 2.German : habitational name for someone from Gill near Neuss, in the Rhineland.Jewish (eastern Ashkenazic) : from the Yiddish male personal name Hiller, a variant of Hillel. The initial G is due to Russian influence, since Russian has no h and alters h to g in borrowed words.
Boy/Male
Czechoslovakian
Miller.
Surname or Lastname
English (chiefly Gloucestershire and Worcestershire)
English (chiefly Gloucestershire and Worcestershire) : variant of Millward.French (northern) : from a Germanic personal name composed of the elements mil ‘good’, ‘gracious’ + hard ‘hardy’, ‘brave’, ‘strong’.Southern French : from a variant spelling of Occitan milhar ‘millet field’ (from mil ‘millet’).
Surname or Lastname
English (northern and eastern)
English (northern and eastern) : variant spelling of Milner.
MILLERS RECURRENCE-ALGORITHM
MILLERS RECURRENCE-ALGORITHM
Boy/Male
Indian
Extremely patient
Male
Spanish
Spanish form of Latin Ulixes, probably ULISES means "to be angry, to hate."
Boy/Male
German, Hawaiian, Hebrew, Hindu, Indian
A Man from Judah; A Jew; Praise of the Lord
Boy/Male
Indian, Malayalam, Tamil
King of Chera
Boy/Male
Hindu, Indian
Offspring; Strong
Girl/Female
Tamil
Benevolence
Female
English
Variant spelling of English Trudy, TRUDI means "spear strength."
Surname or Lastname
English
English : variant of or patronymic form of Grubb.
Surname or Lastname
English, German, and Jewish
English, German, and Jewish : altered spelling of Lerner.
Girl/Female
Greek
From the woods.
MILLERS RECURRENCE-ALGORITHM
MILLERS RECURRENCE-ALGORITHM
MILLERS RECURRENCE-ALGORITHM
MILLERS RECURRENCE-ALGORITHM
MILLERS RECURRENCE-ALGORITHM
a.
Running back toward its origin; as, a recurrent nerve or artery.
n.
Recumbence.
n.
Attack; occurrence.
n.
Alt. of Millreis
n.
A Portuguese money of account rated in the treasury department of the United States at one dollar and eight cents; also, a Brazilian money of account rated at fifty-four cents and six mills.
n.
The act of running down; a lapse.
v. i.
To put forth new shoots from the root, or round the bottom of the original stalk; as, wheat or rye tillers; some spread plants by tillering.
n.
Any incident or event; esp., one which happens without being designed or expected; as, an unusual occurrence, or the ordinary occurrences of life.
n.
The act of incurring, bringing on, or subjecting one's self to (something troublesome or burdensome); as, the incurrence of guilt, debt, responsibility, etc.
n.
Alt. of Recurrency
n.
A coming or happening; as, the occurence of a railway collision.
n.
Recumbence.
n.
The act of recurring, or state of being recurrent; return; resort; recourse.
n.
Alt. of Millreis
a.
Twice milled or fulled, to render more compact or fine; -- said of cloth; as, double-milled kerseymere.
n.
The name of several cereal and forage grasses which bear an abundance of small roundish grains. The common millets of Germany and Southern Europe are Panicum miliaceum, and Setaria Italica.
n.
A moth or lepidopterous insect; -- so called because the wings appear as if covered with white dust or powder, like a miller's clothes. Called also moth miller.
n.
See Milreis.
n.
The act of rising again; resurrection.
a.
Returning from time to time; recurring; as, recurrent pains.