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Algorithm for solving boundary value problems of the Eikonal equation
The fast marching method is a numerical method created by James Sethian for solving boundary value problems of the Eikonal equation: | ∇ u ( x ) | = 1
Fast_marching_method
Partitioning a digital image into segments
structures has led to very efficient implementations of this method. The fast marching method has been used in image segmentation, and this model has been
Image_segmentation
and A. Vladimirsky. Fast two-scale methods for Eikonal equations. SIAM J. on Scientific Computing 34/2: A547-A578, 2012. [1] Fast marching method v t e
Fast_sweeping_method
Non-linear partial differential equation encountered in problems of wave propagation
introduced by Kimmel and Sethian in 1998. Sethian's fast marching method (FMM) was the first "fast and efficient" algorithm created to solve the Eikonal
Eikonal_equation
Distance from a point to the boundary of a set
include the efficient fast marching method, fast sweeping method and the more general level-set method. For voxel rendering, a fast algorithm for calculating
Signed_distance_function
Algorithm for finding shortest paths
graphs, where the priority queue degenerates into a FIFO queue. The fast marching method can be viewed as a continuous version of Dijkstra's algorithm which
Dijkstra's_algorithm
Data structure for integer priorities
numerical methods for the solution of differential equations, untidy priority queues have been used to prioritize the steps of the fast marching method for
Bucket_queue
American mathematician
He maintains the "level set methods and fast marching methods" webpage [2], which is a popular resource for these methods, and provides a variety of applets
James_Sethian
similar to shock capturing Split-step method Fast marching method Orthogonal collocation Lattice Boltzmann methods — for the solution of the Navier-Stokes
List of numerical analysis topics
List_of_numerical_analysis_topics
Conceptual framework used in numerical analysis of surfaces and shapes
Methods and Dynamic Implicit Surfaces. Springer-Verlag. ISBN 978-0-387-95482-0. Sethian, James A. (1999). Level Set Methods and Fast Marching Methods :
Level-set_method
2023 film by Louis Leterrier
Fast X (also known as Fast & Furious 10) is a 2023 American action film directed by Louis Leterrier from a screenplay by Dan Mazeau and Justin Lin, both
Fast_X
Means by which a person dies by suicide
A suicide method is any means by which a person ends or attempts to end their life. Suicide attempts do not always result in death, and a non-fatal suicide
Suicide_methods
Religious practice
faith-based fasting. Examples from the Abrahamic religions include Lent in Christianity; Ramadan in Islam; Yom Kippur, Tisha B'av, Fast of Esther, Fast of Gedalia
Religious_fasting
analysis companies. Kimmel's contributions include the development of fast marching methods for triangulated manifolds (together with James Sethian), the geodesic
Ron_Kimmel
Willing abstinence from, or reduced consumption of, food and/or drink
situation. Fasting is often used to make a political statement, to protest, or to bring awareness to a cause. A hunger strike is a method of non-violent
Fasting
Fast & Furious (also known as The Fast and the Furious) is an American action film series centered on street racing, heists, spies, and family. The following
List of Fast & Furious characters
List_of_Fast_&_Furious_characters
Percussion playing technique
grip is almost exclusively used to play the snare drum, especially the marching snare drum, and the jazz drum kit. Traditional grip is more popular in
Grip_(percussion)
Various systems to schedule meals
and non-fasting over a given period. Methods of intermittent fasting include alternate-day fasting, periodic fasting, such as the 5:2 diet, and daily time-restricted
Intermittent_fasting
Algorithm for finding zeros of functions
In numerical analysis, the Newton–Raphson method, also known simply as Newton's method, named after Isaac Newton and Joseph Raphson, is a root-finding
Newton's_method
Type of restaurant
A fast-food restaurant, also known as a quick-service restaurant (QSR) within the industry, is a specific type of restaurant that serves fast-food cuisine
Fast-food_restaurant
called voxels) Marching squares: generates contour lines for a two-dimensional scalar field Marching tetrahedrons: an alternative to Marching cubes Discrete
List_of_algorithms
Numerical method for solving physical or engineering problems
Finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical
Finite_element_method
Discrete Fourier transform algorithm
overlap–save methods), fast algorithms for discrete cosine or sine transforms (e.g. fast DCT used for JPEG and MPEG/MP3 encoding and decoding), fast Chebyshev
Fast_Fourier_transform
Probabilistic problem-solving algorithm
coverage and normally have a faster order of convergence than Monte Carlo simulations using random or pseudorandom sequences. Methods based on their use are
Monte_Carlo_method
Fast method for calculating the digits of π
The Chudnovsky algorithm is a fast method for calculating the digits of π, based on Ramanujan's π formulae. Published by the Chudnovsky brothers in 1988
Chudnovsky_algorithm
Interplay between observation, experiment, and theory in science
The scientific method is an empirical method for acquiring knowledge through careful observation, rigorous skepticism, hypothesis testing, and experimental
Scientific_method
American fast food company founders
the Speedee Service System to produce their meals, a method that became the standard for the fast food industry. After hiring Ray Kroc as their franchise
Richard_and_Maurice_McDonald
Physical property of certain bacterial, protozoal, and eukaryotic cells
identify acid-fast bacteria is the Ziehl–Neelsen stain, in which acid-fast species appear bright red against a blue background. Another method is the Kinyoun
Acid-fastness
Approach to finding numerical solutions of ordinary differential equations
In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary
Euler_method
2003 film by John Singleton
2 Fast 2 Furious is a 2003 American action film directed by John Singleton from a screenplay by Michael Brandt and Derek Haas, based on a story by Brandt
2_Fast_2_Furious
Optimization algorithm
first-order method for large-scale problems. For constrained or non-smooth problems, Nesterov's FGM is called the fast proximal gradient method (FPGM), an
Gradient_descent
Medical mnemonic of stroke symptoms
in the prehospital setting. BE-FAST has shown promise and is currently being studied as an alternative method to the FAST acronym. B - balance degradation
FAST_(stroke)
Bacteriological technique
Friedrich Neelsen (1854–1898) during the late 19th century. The acid-fast staining method, in conjunction with auramine phenol staining, serves as the standard
Ziehl–Neelsen_stain
Numerical technique for bioelectromagnetic modeling
This formulation is naturally combined with fast multipole method (FMM) acceleration, and the entire method is known as charge-based BEM-FMM. The combination
Charge based boundary element fast multipole method
Charge_based_boundary_element_fast_multipole_method
One-dimensional approximation to a shape
Press, ISBN 0-12-637240-3. Sethian, J. A. (1999), Level Set Methods and Fast Marching Methods, Cambridge University Press, Bibcode:1999lsmf.book.....S,
Topological_skeleton
Mass-produced food designed for rapid service and consumption
Fast food is a type of mass-produced food designed for commercial resale, with a strong priority placed on speed of service. Fast food is a commercial
Fast_food
Periodicity computation method
of Queen's University in Kingston, Ontario, developed the "fast orthogonal search" method of more quickly finding a near-optimal decomposition of spectra
Least-squares spectral analysis
Least-squares_spectral_analysis
1982 film directed by Amy Heckerling
Fast Times at Ridgemont High is a 1982 American coming-of-age comedy-drama film directed by Amy Heckerling in her feature directorial debut. The screenplay
Fast_Times_at_Ridgemont_High
2001 soundtrack album by various artists
The Fast and the Furious: Original Motion Picture Soundtrack is the first of two soundtracks to Rob Cohen's 2001 action film The Fast and the Furious
The Fast and the Furious (soundtrack)
The_Fast_and_the_Furious_(soundtrack)
Technique in computer graphics
object can be solved by a technique called marching triangles. This provides a faster alternative to other methods for the same problem of surface reconstruction
Marching_triangles
2019 film by David Leitch
Fast & Furious Presents: Hobbs & Shaw (or simply Hobbs & Shaw) is a 2019 American buddy action comedy film directed by David Leitch from a script by Chris
Hobbs_&_Shaw
Making fashion trends quickly and cheaply available to consumers
response manufacturing methods, increased usage of low-cost labor from Asia, and cheaper petroleum-based synthetic fibers. Fast fashion particularly came
Fast_fashion
Interactive forecasting method
Delphi method, or Delphi technique (/ˈdɛlfaɪ/ DEL-fy; also known as Estimate–Talk–Estimate, or ETE), is a structured communication technique, or method, originally
Delphi_method
Branch of physics
element methods); matrix products (when using transfer matrix methods); calculating numerical integrals (when using the method of moments); using fast Fourier
Computational electromagnetics
Computational_electromagnetics
Form of protest or political activism
A hunger strike is a method of non-violent resistance where participants fast as an act of political protest, usually with the objective of achieving a
Hunger_strike
Technique used to enhance visual contrast of specimens observed under a microscope
Morande PE, Zolessi FR (September 2014). "A fast, low cost, and highly efficient fluorescent DNA labeling method using methyl green". Histochemistry and Cell
Staining
Application layer protocol
lower latency for real-world web pages and loads faster than HTTP/2, in some cases over three times faster than HTTP/1.1, which is still commonly the only
HTTP
Educational company based in Japan
educational network based in Japan and created by Toru Kumon. It uses his "Kumon Method" to teach mathematics and reading, primarily to young students. Japanese
Kumon
American influencer
commentary, and relatable monologues. He is known for his video series "Fast Food Secrets Club". As of 2025, he had over 14 million followers, and another
Jordan_Howlett
Mathematical optimization algorithm
In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose
Conjugate_gradient_method
2011 film by David Cronenberg
A Dangerous Method is a 2011 historical drama film directed by David Cronenberg. The film stars Keira Knightley, Viggo Mortensen, Michael Fassbender, Sarah
A_Dangerous_Method
radial velocity method, it does not require an accurate spectrum of a star, and therefore can be used more easily to find planets around fast-rotating stars
Methods of detecting exoplanets
Methods_of_detecting_exoplanets
Pairwise-comparison electoral system
but the "constructive" definition executes much faster (small polynomial time). The Schulze method resolves votes as follows: At each stage, we proceed
Condorcet_method
Nuclear reactor generating more fissile material than it consumes
reprocessing methods used leave a large fraction of the transuranics in the final waste stream, this advantage would be greatly reduced. The FBR's fast neutrons
Breeder_reactor
American quack, fraud, swindler and serial killer
The Science of Fasting, she studied under Edward Hooker Dewey, MD, a well-known proponent of fasting. Hazzard developed a fasting method that she claimed
Linda_Hazzard
Algorithms for calculating square roots
initial estimate, the faster the convergence. For Newton's method, a seed somewhat larger than the root will converge slightly faster than a seed somewhat
Square_root_algorithms
Ethernet standards that carry data at the nominal rate of 100 Mbit/s
code method used. Fast Ethernet is sometimes referred to as 100BASE-X, where X is a placeholder for the FX and TX variants. IEEE 802.2 refers to Fast Ethernet
Fast_Ethernet
Search algorithm finding the position of a target value within a sorted array
apply binary search. There are specialized data structures designed for fast searching, such as hash tables, that can be searched more efficiently than
Binary_search
Performances by American actor
successful role is as Luke Hobbs in the Fast & Furious franchise; he first appeared as the character in Fast Five (2011) and is credited with breathing
Dwayne_Johnson_filmography
Method of scheduling activities
The critical path method (CPM), or critical path analysis (CPA), is an algorithm for scheduling a set of project activities. A critical path is determined
Critical_path_method
algorithm Local coordinates Low-discrepancy sequence Low poly Marching cubes Marching squares Marching tetrahedra Mask (computing) Mesh generation Metropolis
List of computer graphics and descriptive geometry topics
List_of_computer_graphics_and_descriptive_geometry_topics
functional in some situations. The fast extrapolation method can get the same results as the other extrapolation methods, and can be applied to the above
Interior_reconstruction
Cooking method and apparatus
various cooking methods, employing live fire and smoke to cook food. The term is applied to the devices associated with those methods, the broader cuisines
Barbecue
American actor (born 1964)
worldwide. Born into the Coppola family, Cage began his career in films such as Fast Times at Ridgemont High (1982) and Valley Girl (1983), as well as various
Nicolas_Cage
Method for approximate evaluation of integrals
approximations are used in the integrated nested Laplace approximations method for fast approximations of Bayesian inference. Let the function f ( x ) {\displaystyle
Laplace's_method
Algorithm to multiply two numbers
multiplication, unleashing a flood of research into fast multiplication algorithms. This method uses three multiplications rather than four to multiply
Multiplication_algorithm
Bowling technique in cricket
Fast bowling (also referred to as pace bowling) is a type of bowling in cricket, in which the ball is delivered at high speed. The fastest bowlers bowl
Fast_bowling
Time management method
The Pomodoro Technique is a time management method developed by Francesco Cirillo in the late 1980s. It uses a kitchen timer to break work into intervals
Pomodoro_Technique
Simulation technique in computer hardware design
Static timing analysis (STA) is a simulation method of computing the expected timing of a synchronous digital circuit without requiring full circuit-simulation
Static_timing_analysis
Root-finding method
quasi-Newton method. If we compare Newton's method with the secant method, we see that Newton's method converges faster (order 2 against order the golden ratio
Secant_method
Solving physical puzzles with speed
older solvers. However, there is debate as to whether the ZB method is actually faster overall, since by cutting down on the steps required to solve
Speedcubing
Chinese character input method
The Stroke Count Method (Chinese: 笔画; pinyin: bǐ huà), Wubihua method, Stroke input method or Bihua IME (Chinese: 五笔画输入法; pinyin: wǔ bǐhuà shūrù fǎ or
Stroke_count_method
Umbrella term for certain approaches to software development
methodology is more flexible than traditional modeling methods, making it a better fit in a fast-changing environment. It is part of the agile software
Agile_software_development
Japanese organizing consultant, author, and television show host
the United States and the United Kingdom, the profile of Kondo and her methods were greatly promoted by the success of the Netflix series Tidying Up with
Marie_Kondo
Planning time spent on specific activities
which indicates in which order to execute the tasks. The latter method is generally faster, allowing the tasks to be recorded more quickly. Various writers
Time_management
Class of astringent, bitter plant polyphenolic chemical compounds
Heru; Li, Weibin (2006–2007). Study on Fast Determination Content of Condensed Tannin Using Stiasny Method (Report). Guangdong Chemical Industry. Archived
Tannin
Process of determining the nucleic acid sequence
currents has the potential to sequence orders of magnitude faster than ionic current methods and the sequencing of several DNA oligomers and micro-RNA
DNA_sequencing
Authentication protocol for the point-to-point protocol
an EAP-FAST module for Windows Vista and later operating systems which have an extensible EAPHost architecture for new authentication methods and supplicants
Extensible Authentication Protocol
Extensible_Authentication_Protocol
Social media platform owned by Meta
April 17, 2021. Carr, Austin (March 25, 2014). "Instagram Testing Facebook Places Integration To Replace Foursquare". Fast Company. Archived from the original
Methods used to find numerical solutions of ordinary differential equations
Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations
Numerical methods for ordinary differential equations
Numerical_methods_for_ordinary_differential_equations
Indian fast breeder nuclear reactor design
The Prototype Fast Breeder Reactor (PFBR) is a 500 MWe pool type sodium-cooled, fast breeder reactor commissioned at the same site as the Madras Atomic
Prototype Fast Breeder Reactor
Prototype_Fast_Breeder_Reactor
Marching group
commands are generally used with a group that is marching, most often in military foot drills or in a marching band. Drill commands are usually heard in major
Drill_commands
Basic method for pseudo-random number sampling
moderate-degree polynomials, and in fact the method of doing this is fast enough that inversion sampling is now the default method for sampling from a normal distribution
Inverse_transform_sampling
Kinetic energy of an unbound neutron
A fast neutron is a free neutron with a kinetic energy level close to 1 MeV (100 TJ/kg), hence a speed of 14,000 km/s or higher. They are named fast neutrons
Neutron_temperature
Concentration of glucose present in the blood (Glycaemia)
skin. Both methods, as of 2023, cost hundreds of dollars or euros per year for supplies needed.[citation needed] Glucose testing in a fasting individual
Blood_sugar_level
Algorithm for polynomial evaluation
take advantage of instruction-level parallelism. Horner's method is a fast, code-efficient method for multiplication and division of binary numbers on a
Horner's_method
Eleventh day of the lunar fortnight
more liberal form of fasting is followed by most devotees. There are different ways to observe the Ekadashi fasting in this method, ranging from complete
Ekadashi
Type of deterministic method for multivariate interpolation
Inverse distance weighting (IDW) is a type of deterministic method for multivariate interpolation with a known homogeneously scattered set of points. The
Inverse_distance_weighting
3D printing technique
that it can create objects up to 100 times faster than commercial three dimensional (3D) printing methods. CLIP objects have smooth sides, unlike 2015
Continuous Liquid Interface Production
Continuous_Liquid_Interface_Production
Abbreviated symbolic writing method
abbreviated symbolic writing method that increases speed and brevity of writing as compared to longhand, a more common method of writing a language. The
Shorthand
Battleship that emphasizes speed without undue compromises in armor or armament
was the principal challenge of fast battleship design. While increasing length-to-beam ratio was the most direct method of attaining a higher speed, this
Fast_battleship
American businessman (born 1964)
from the original on March 20, 2018. Retrieved March 7, 2018. Fishman, Charles (January 31, 2001). "Face Time With Jeff Bezos". Fast Company. Archived from
Jeff_Bezos
American mathematician (born 1957)
computer scientist. He is co-inventor with Vladimir Rokhlin Jr. of the fast multipole method (FMM) in 1987, recognized as one of the top-ten algorithms of the
Leslie_Greengard
Breaded deboned chicken meat pieces
finding a way to make a coating adhere, chicken nuggets have become a popular fast food restaurant item, and are widely sold frozen for home use. There are
Chicken_nugget
Type of information retrieval using LLMs
or other document look-up process to help LLMs stick to the facts." This method helps reduce AI hallucinations, which have caused chatbots to describe policies
Retrieval-augmented generation
Retrieval-augmented_generation
Temporary abstinence from addictive technologies
Dopamine fasting is the general practice of abstaining from any impulsive and behavioral addictions in order to cope with such addictions and thus attempt
Dopamine_fasting
Astronomical high energy transient pulse
radio astronomy, a fast radio burst (FRB) is a transient radio wave of duration ranging from a fraction of a millisecond, for an ultra-fast radio burst, to
Fast_radio_burst
Optimization algorithm
Stochastic gradient descent (often abbreviated SGD) is an iterative method for optimizing an objective function with suitable smoothness properties (e
Stochastic_gradient_descent
Method of calculating ray-triangle intersections in 3D space
algorithm, named after its inventors Tomas Möller and Ben Trumbore, is a fast method for calculating the intersection of a ray and a triangle in three dimensions
Möller–Trumbore intersection algorithm
Möller–Trumbore_intersection_algorithm
Decrease in blood sugar
may result in headache, tiredness, clumsiness, trouble talking, confusion, fast heart rate, sweating, shakiness, nervousness, hunger, loss of consciousness
Hypoglycemia
FAST MARCHING-METHOD
FAST MARCHING-METHOD
Surname or Lastname
English
English : variant spelling of Machen.Spanish (MachÃn) : probably a nickname from machÃn ‘boor’, ‘lout’, often applied to a blacksmith’s apprentice.French : nickname from Old French machin ‘scheming’.
Surname or Lastname
English
English : habitational name from a place named in Old English with fēorðing ‘fourth (part)’, ‘quarter’, being the fourth part of a larger administrative area. There are fifteen or more minor places with this name in southern England. As a surname, it may also denote someone who paid a farthing in rent, from the same word in the sense ‘farthing’, ‘quarter of a penny’.English : from the Old Norse personal name Farþegn, composed of the elements fara ‘to go’ + þegn ‘warrior’, ‘hero’.
Girl/Female
Latin
Of Mars. Feminine of Marcus. Mars was mythological Roman god of fertility also identified with...
Surname or Lastname
English (East Anglia)
English (East Anglia) : unexplained.
Surname or Lastname
German
German : probably a habitational name from Haste near Wunstorf or Osnabrück.Dutch : nickname from Middle Dutch haest ‘hasty’.Swedish : soldier’s name, from hast ‘haste’, ‘hurry’.English (Lancashire and Yorkshire) : reduced form of Hayhurst.
Surname or Lastname
English
English : variant of Markin.
Surname or Lastname
English and French
English and French : variant of Marchand.John Marchant (c.1600–c.1668) was in Newport, RI, before 1638. In that year he moved to Braintree, MA, then to Watertown, MA (1642), and finally to Yarmouth, MA (1648). His descendants included many sea captains and other prominent people.
Surname or Lastname
English
English : topographic name for someone who lived in the eastern part of a town or settlement, or outside it to the east, or a regional name for someone who had migrated from the east of a place. As an American family name, this surname has absorbed various other European names with similar meaning.
Girl/Female
Afghan, Arabic, Bengali, Indian, Kannada, Marathi, Muslim
Like; Equal; Matching
Surname or Lastname
English (East Anglia)
English (East Anglia) : unexplained.
Surname or Lastname
English (East Anglia)
English (East Anglia) : unexplained.
Boy/Male
Arabic, Muslim, Pashtun
Gul - Flowers; Mast - Excitement
Girl/Female
Muslim
Like. Equal. Matching.
Female
Egyptian
, Child of Bast.
Surname or Lastname
English (East Anglia)
English (East Anglia) : metonymic occupational name for a cobbler, or perhaps a metonymic occupational name for a maker of cobblers’ lasts (see Laster).German and Jewish (Ashkenazic) : metonymic occupational name for a porter, from Middle High German last; German Last or Yiddish last ‘burden’, ‘load’.Dutch : metonymic occupational name as in 2, from Middle Dutch last ‘load’, ‘burden’; or a nickname for an awkward character, from Dutch last ‘trouble’, ‘nuisance’.French : habitational name from a place so named in Puy-de-Dôme.
Girl/Female
Hindu, Indian, Sanskrit
Goddess Durga
Surname or Lastname
English
English : variant of Merlin.
Girl/Female
Indian, Tamil
Goddess Parvati
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Tamil, Telugu
Ray of Light
Male
Polish
Polish form of Roman Latin Martinus, MARCIN means "of/like Mars."
FAST MARCHING-METHOD
FAST MARCHING-METHOD
Female
Egyptian
, the daughter of Prince Psametik.
Biblical
a hill
Boy/Male
English Teutonic
Hero's peace.
Boy/Male
Hindu, Indian
Beautiful; Auspicious; Lucky; Pretty
Boy/Male
Hindu
Wise, Ruler
Girl/Female
British, Christian, English, Latin
Female Version of Horace; Derived from the Roman Clan Name Horatius; Time Keeper
Girl/Female
American, Anglo, Australian, British, English
Born at Easter; Goddess of the Dawn; Easter Time
Girl/Female
Indian
Protector
Girl/Female
English
Glory.
Boy/Male
Arabic, Muslim
Help; Succour
FAST MARCHING-METHOD
FAST MARCHING-METHOD
FAST MARCHING-METHOD
FAST MARCHING-METHOD
FAST MARCHING-METHOD
v. i.
A time of fasting, whether a day, week, or longer time; a period of abstinence from food or certain kinds of food; as, an annual fast.
a.
Toward the rising sun; or toward the point where the sun rises when in the equinoctial; as, the east gate; the east border; the east side; the east wind is a wind that blows from the east.
v. t.
To gripe with the fist.
a.
In a fast or rapid manner; quickly; swiftly; extravagantly; wildly; as, to run fast; to live fast.
v.
Given to pleasure seeking; disregardful of restraint; reckless; wild; dissipated; dissolute; as, a fast man; a fast liver.
n.
The week last past; last week.
v. i.
To cast anchor; to become fast.
v.
Firm in adherence; steadfast; not easily separated or alienated; faithful; as, a fast friend.
v.
Permanent; not liable to fade by exposure to air or by washing; durable; lasting; as, fast colors.
adv.
On the last night past.
v.
Moving rapidly; quick in mition; rapid; swift; as, a fast horse.
n.
The last night; the night last past.
n.
The year last past; last year.
v. t.
To strike with the fist.
imp. & p. p.
of Cast
v.
Firmly fixed; closely adhering; made firm; not loose, unstable, or easily moved; immovable; as, to make fast the door.
v. t.
To shape with a last; to fasten or fit to a last; to place smoothly on a last; as, to last a boot.
n.
The fist.
a.
Exploring thoroughly; scrutinizing; penetrating; trying; as, a searching discourse; a searching eye.
a.
In a fast, fixed, or firmly established manner; fixedly; firmly; immovably.